6x+18y+6z=24, -x-3y-2z=-4, 2x+6y+2z=8

Answers

Answer 1

Answer:

Please check the explanation below.

Step-by-step explanation:

Given the equations

[tex]6x+18y+6z=24,\:-x-3y-2z=-4,\:2x+6y+2z=8\:\:[/tex]

Steps to solve

[tex]\begin{bmatrix}6x+18y+6z=24\\ -x-3y-2z=-4\\ 2x+6y+2z=8\end{bmatrix}[/tex]

[tex]\mathrm{Subsititute\:}x=4-3y-z[/tex]

[tex]\begin{bmatrix}-\left(4-3y-z\right)-3y-2z=-4\\ 2\left(4-3y-z\right)+6y+2z=8\end{bmatrix}[/tex]

As

[tex]-\left(4-3y-z\right)-3y-2z=-4[/tex]

[tex]-z-4=-4[/tex]

and

[tex]2\left(4-3y-z\right)+6y+2z=8[/tex]

[tex]8=8[/tex]

so

[tex]\begin{bmatrix}-z-4=-4\\ 8=8\end{bmatrix}[/tex]

Isolating z for [tex]-z-4=-4[/tex]

[tex]-z-4=-4[/tex]

[tex]-z=0[/tex]

[tex]\frac{-z}{-1}=\frac{0}{-1}[/tex]

[tex]z=0[/tex]

[tex]\mathrm{For\:}x=4-3y-z[/tex]

[tex]\mathrm{Expressing\:}x\mathrm{\:in\:terms\:of\:}y[/tex]

[tex]x=4-3y-0[/tex]

[tex]x=-3y+4[/tex]

Therefore,

[tex]\mathrm{The\:solutions\:to\:the\:system\:of\:equations\:are:}[/tex]

[tex]x=-3y+4,\:z=0[/tex]


Related Questions

Need help with this question please and thanks

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Answer:

C

Step-by-step explanation:

Because C line has the straighest edge and it's the most consistent

4. What are the different types of auto insurance
plans?

Answers

Answer:

auto liability coverage, uninsured and underinsured motorist coverage, comprehensive coverage, collision coverage, medical payments coverage and personal injury protection

Step-by-step explanation:

How did Dana's profit change? Complete
the sentence.
Dana's profit ?
by $14 from
Saturday to Sunday.

Answers

Answer:increasing

Step-by-step explanation:

Answer:

Increased I did the Quiz Pratice: Adding and Subtrating Integers- Quiz-Level G

Step-by-step explanation: LOL I knew the lesson

Mark and Nora both work at the same pet store. The inequality y less than or equal too 2x relates x, the number of hours Mark works each week, and y, the number of hours that Nora works. Which ordered pair must be included in the solution set of the inequality when interpreted in the context of the problem? please help
(–7, 20)
(0, 0)
(8, 2)
(13, –28)

Answers

Answer:

y≤2x

Step-by-step explanation:

answer in comments

Find the equation of the linear function x 0 1 2 3 4 y -4 -2 0 2 4

Answers

Answer:

its counting down

Step-by-step explanation:

because it was in the positives and went down to the negatives

please help asap i just need the relationship and measure of x

Answers

Answer:

if it asking for the type of angle the both are obtuse and the fisrt measure is 135 and the second is 101

Step-by-step explanation:

The relation between 135 and x is corresponding angles.

The value of x is 135 degree.

because the corresponding angles are equal.

Please help me find the area

Answers

Answer:

[tex]8x^{2} +14x+6[/tex]

Step-by-step explanation:

The formula for the area of rectangle is length times width:

[tex](2x+2)(4x+3)\\[/tex]

Use FOIL method:

[tex]8x^{2} +6x+8x+6\\8x^{2} +4x+6[/tex]

1+1 then divide by 8

Answers

Answer:

0.25

Step-by-step explanation:

How does Indian reservation have an effect on the Right of Occupancy
please answer like this:
the indian reservation has an effect on the right of occupancy by....

then add your answer:)

Answers

Step-by-step explanation:

hope it was helpful....

Kenny went golfing with his dad. Kenny had a score of -2 and his dad had a score of +8. How many more shots did Kenny’s dad take?

Answers

Answer:

4! am i right or am i right Owo

Step-by-step explanation:

the dad made 10 more shots than kenny

Use the Distributive Property to Expand the Expression
1) 8 ( b + 5 )

Answers

Answer:

8b + 40

Step-by-step explanation:

8( b + 5 )

8×b + 8×5

8b+40

this is my home work plese help

Answers

Answer: 345 dollars a week

Step-by-step explanation:

Answer:

345.63

Step-by-step explanation:

39.5*8.75=345.625

345.625=345.63

The longest leg of a right triangle is 12 feet and another side is 5 feet. Find the length of the remaining side.​

Answers

Answer:

10.98 (approximately)

if you wan the exact answer, type into the google search bar:

"sqrt 119"

Step-by-step explanation:

in a right triangle, the longest leg is called the hypotenuse. To find the missing side, you need to use the Pythagorean theorem.

"a^2+b^2=c^2"

c = the hypotenuse

a and be are the other legs.

plug in the numbers.

5^2+b^2 = 12^2

25 + b^2 = 144

b^2 = 119

b = 10.98 (approximately)

What is the measure of \large \angle V?

Answers

Answer:

THe interior angles of any triangle equal 180

THerefore 48+87+v=180

48+87+v=180

87+v=132

v=45

Step-by-step explanation:

Chang knows one side of a triangle is 13 cm. Which set of two sides is possible for the lengths of the other two
sides of this triangle?
5 cm and 8 cm
6 cm and 7 cm
7 cm and 2 cm
8 cm and 9 cm

Answers

Answer:

8cm and 9cm

Step-by-step explanation:

The other sides are not greater than 13.

A: 5 + 8 = 13

B: 6 + 7 = 13

C: 7 + 2 = 9

However, D is greater than 13 and is the correct answer.

D: 8 + 8 = 16.

This answer would b 8cm and 9cm because

What is the y intercept? 7x+y=10

Answers

Answer:

the y intercept is y

Step-by-step explanation:

because we have the variable already/////

What is the equation of a line that has a slope of 2 and passes through point (-6, 3)?

Answers

Step-by-step explanation:

m= 2

x1 = -6

y1 = 3

Applying the formula,

y-y1 = m(x-x1);

we have,

y - 3 = 2(x -(-6))

y- 3 = 2(x + 6)

y - 3 = 2x + 12

y -2x -3 -12 = 0

y -2x -15 = 0

Therefore the equation of the line is;

2x - y + 15 = 0

Oil is pumped into a tank at a rate of Q(t)=45-t gallons per minute where time is t is measured in minutes how many gallons are in the tank after 30 minutes

Answers

Answer:

15 gallons

Step-by-step explanation:

Given that:

Pumping rate is modeled by the equation :

Q(t)=45-t gallons per minute ; where t is in minutes

Number of gallons in tank after 30 minutes ;

Q(t)=45-t

Q(30) = 45 - 30

Q(30) = 15

Hence, Number of gallons in tank after 30 minutes is 15 gallons

I ONLY HAVE 5 MIN TO ANSWER PLEASE HELP ME !!!!!!!!!!!

How do you determine which values to multiply when you apply the distributive property?

WILL MARK BRAINLIEST!!!

Answers

Here it is:                                      

Distributive Property

11. Health. Sherri is considering joining a health club. To be a member of Roman's Gym, she would
have to pay a sign-up fee of $49.99 and then $25 per month. Another club, Athens Fitness
Center, charges less per month (only $18) but has a $126.99 sign-up fee. After how many
months of membership would the total paid to each club be the same?

Answers

It would take 11 months of membership for the total money paid to each club to be the same.

What is an equation?

An equation is an expression that shows the relationship between two or more numbers and variables.

A variable can either be dependent or independent. A dependent variable depend on other variable while an independent variable does not depend on other variables.

Let x represent the number of months subscribed. Hence,

For Roman's gym:

Total payment = 25x + 49.99

For Athens Fitness:

Total payment = 18x + 126.99

For both clubs to have the same payment:

25x + 49.99 = 18x + 126.99

7x = 77

x = 11

It would take 11 months of membership for the total money paid to each club to be the same.

Find out more on equation at: https://brainly.com/question/13763238

#SPJ1

-2/5x-9<9/10 Solve the inequality. Please help. YOU'LL BE THE BRAINLYEST!!!

Answers

Answer:

x>-99/4

Step-by-step explanation:

Sarah tosses a coin and spins a spinner

Answers

Answer:

Good for her ig

Step-by-step explanation:

During a snowstorm, the temperature drops from 0°F to -12°F in 3 hours. On
average, by how many degrees is the temperature changing per hour?

Answers

Answer:D.

-4°F

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

d

Find the variance of: 2 4 5 6 7 9 10

Answers

Add 2 two time and add 1 three times then add 2 and then 1. Maybe

Answer:

s  =  7.811  ¯  6

Step-by-step explanation:

x =  2  + 4  +  5  +  6  +  7  +  9  +  10 /7

¯ x = 43 /7

s = ( 2 − 6.1 ) 2 + ( 4 − 6.1 ) 2 + ( 5 − 6.1 ) 2 + ( 6 − 6.1 ) 2 + (7 − 6.1 ) 2 + ( 9 − 6.1 ) 2 + ( 10 − 6.1 ) 2/ 7 − 1

s = 7.811 ¯ 6

Write an equation of a line perpendicular to y=-4x+9 that has a y-intercept of 7.
Use y=mx=b

Answers

Answer:

9

Step-by-step explanation:

easy

Solve the system of equation 0.4x – 3y = 7

3x + 14y = 10 using Cramer's Rule.

Answers

Answer:

for 0.4x – 3y = 7

Step-by-step explanation:

The answer is Changes made to your input should not affect the solution:

(1): "0.4" was replaced by "(4/10)".

Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

                    (4/10)*x-3*y-(7)=0

STEP

1

:

           2

Simplify   —

           5

Equation at the end of step

1

:

   2                

 ((— • x) -  3y) -  7  = 0

   5                

STEP

2

:

Rewriting the whole as an Equivalent Fraction

2.1   Subtracting a whole from a fraction

Rewrite the whole as a fraction using  5  as the denominator :

         3y     3y • 5

   3y =  ——  =  ——————

         1        5  

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

Adding fractions that have a common denominator :

2.2       Adding up the two equivalent fractions

Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

2x - (3y • 5)     2x - 15y

—————————————  =  ————————

      5              5    

Equation at the end of step

2

:

 (2x - 15y)    

 —————————— -  7  = 0

     5        

STEP

3

:

Rewriting the whole as an Equivalent Fraction :

3.1   Subtracting a whole from a fraction

Rewrite the whole as a fraction using  5  as the denominator :

        7     7 • 5

   7 =  —  =  —————

        1       5  

Adding fractions that have a common denominator :

3.2       Adding up the two equivalent fractions

(2x-15y) - (7 • 5)     2x - 15y - 35

——————————————————  =  —————————————

        5                    5      

Equation at the end of step

3

:

 2x - 15y - 35

 —————————————  = 0

       5      

STEP

4

:

When a fraction equals zero :

4.1    When a fraction equals zero ...

Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.

Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.

Here's how:

 2x-15y-35

 ————————— • 5 = 0 • 5

     5    

Now, on the left hand side, the  5  cancels out the denominator, while, on the right hand side, zero times anything is still zero.

The equation now takes the shape :

  2x-15y-35  = 0

Equation of a Straight Line

4.2     Solve   2x-15y-35  = 0

Tiger recognizes that we have here an equation of a straight line. Such an equation is usually written y=mx+b ("y=mx+c" in the UK).

"y=mx+b" is the formula of a straight line drawn on Cartesian coordinate system in which "y" is the vertical axis and "x" the horizontal axis.

In this formula :

y tells us how far up the line goes

x tells us how far along

m is the Slope or Gradient i.e. how steep the line is

b is the Y-intercept i.e. where the line crosses the Y axis

The X and Y intercepts and the Slope are called the line properties. We shall now graph the line  2x-15y-35  = 0 and calculate its properties

Graph of a Straight Line :

 

Calculate the Y-Intercept :

Notice that when x = 0 the value of y is 7/-3 so this line "cuts" the y axis at y=-2.33333

 y-intercept = 35/-15 = 7/-3  = -2.33333

Calculate the X-Intercept :

When y = 0 the value of x is 35/2 Our line therefore "cuts" the x axis at x=17.50000

 x-intercept = 35/2  = 17.50000

Calculate the Slope :

Slope is defined as the change in y divided by the change in x. We note that for x=0, the value of y is -2.333 and for x=2.000, the value of y is -2.067. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of -2.067 - (-2.333) = 0.267 in y. (The change in y is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)

   Slope     =  0.267/2.000 =  0.133

Geometric figure: Straight Line

 Slope = 0.267/2.000 = 0.133

 x-intercept = 35/2 = 17.50000

 y-intercept = 35/-15 = 7/-3 = -2.33333

Please write the asnwerr belowww

Answers

Answer:

The original length of the new candle is 10 inches

Step-by-step explanation:

The form of the linear function is y = m x + b, where

m is the slope of the lineb is the y-intercept value y at x = 0

L represents the length of the candle remeaning unburned in inches

t represents the time after the candle was lit in hours

∵ The relationship between L and t is linear

→ Put it in the form of the equation above

L = m t + b, where b is the original length of the new candle

→ Use the table to find m

∵ m = [tex]\frac{L2-L1}{t2-t1}[/tex]

∵ (1, 9) and (6, 4) are two points in the given table

t1 = 1 and L1 = 9

t2 = 6 and L2 = 4

→ Substitute them in the rule of m above

∵ m = [tex]\frac{4-9}{6-1}[/tex] = [tex]\frac{-5}{5}[/tex] = -1

m = -1

→ Substitute it in the equation above

∵ L = -1(t) + b

∴ L = -t + b

→ To find b substitute t by 1 and L by 9

∵ 9 = -(1) + b

∴ 9 = -1 + b

→ Add 1 to both sides

∵ 9 + 1 = -1 + 1 + b

10 = b

∵ b is the original length of the new candle

The original length of the new candle is 10 inches

a person is paying $10 per week to a friend to repay a $100 loan

Answers

Answer:

It would take the person 10 weeks to pay the friend back

Step-by-step explanation:

Don't know is this was the question :l

Answer:

y=-10x+100

Step-by-step explanation:

Joe is installing a light fixture on a wall using a 10 foot ladder. A flower garden is planted along the wall, so Joe must place his ladder 6 feet away from the wall. How high up the wall will his ladder reach?

Answers

Answer:

The ladder is 8 feet high up on the wall.

Step-by-step explanation:

Let the height up of the ladder on the wall be represented by h. The ladder leaning on the wall, wall and distance of the foot of ladder from the wall form a right angled triangle.

So, applying the Pythagoras theorem;

[tex]/hyp/^{2}[/tex] = [tex]/adj 1/^{2}[/tex] + [tex]/adj 2/^{2}[/tex]

[tex]/10/^{2}[/tex] = [tex]/6/^{2}[/tex] + [tex]/h/^{2}[/tex]

100 = 36 + [tex]h^{2}[/tex]

so that,

[tex]h^{2}[/tex] = 100 - 36

   = 64

⇒ h = [tex]\sqrt{64}[/tex]

      = 8 feet

The ladder is 8 feet high up on the wall.

What type of solution is "x=0" (one solution, no solution, infinite solutions)? Explain.​

Answers

It is a no solution equation

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