Ren was trying to solve a system of linear equations. He correctly argued that he could replace one equation by the sum of that equation and multiple of the other. He stated that this would produce a system that has the same solution as the original system.
To show this, Ren wrote down a system of equations. He them determined wich othe system of equations would have the same solution as the original system. Ren's original system is shown below.
Answers
Answer:
This what I got.
Hope it helps!
The solution of 1st and 2nd system of equations have solutions same as the main system of equations and 3rd is not same.
What is a system of equations?A set of simultaneous equations, also known as a system of equations or an equation system, is a finite set of equations for which common solutions are sought.
The given equations are;
-2x-5y = -47........(i)
4x-2y = -2
We can simply it, and write;
2x-y = -1
y = 2x+1.....(ii)
Put equation (ii) in (i)
-2x-5(2x+1) = -47
-2x-10x-5 = -47
-12x = -42
x = 7/2
Put value of x in eq (ii)
y = 2(7/2)+1
y = 8
Therefore, the solution of main equation is (7/2, 8)
Solving the other three equations,
1) -14x+y = -41
or, y = -41+14x......(i)
2) 4x-2y = -2
or, 2x-y = -1
y = 2x+1....(ii)
Solving the equations,
2x+1 = -41+14x
12x = 42
x = 7/2
Put x = 7/2, in (ii)
y = 8
Therefore, the solution is (7/2, 8)
We get the solution of main equation is equal to this system of equation.
2) -2x-5y = -47......(i)
6x+3y = 45
or, 2x+y = 15.......(ii)
Solving the equation by elimination,
-4y = -32
y = 8
Put y = 8 in equation (ii)
2x+8 = 15
x = 7/2
Therefore, the solution is (7/2, 8)
Again, we get the solution of main equation is equal to this system of equation.
3) -2x-5y = -47.........(i)
8x-5y = -8.......(ii)
Solving the equations by elimination,
-10x = -39
x = 39/10
Since, value of x is not same as the value of x in main equation, that means, both the system of the equation do not have same solution.
Hence, we get that, the solution of 1st and 2nd system of equations have solutions same as the main system of equations and 3rd is not same.
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Related Questions
Find the explicit formula.
-6, -26,-46,-66, ...
Answers
Answer:
-20
Step-by-step explanation:
as you can see you can still see the 6s, whats the difference between 40 and 20? its 20, its like skip counting but negative, the answer couldve been "20" if it made the number go potitive but its negative so the answer is -20
Juanita is buying a cover for her motorcycle which has a length of 7.5 feet if the covers are only sold in whole foot increments what size covers should Juanita buy
Answers
Answer:
Size of the cover should Juanita buy is 8 feet.
Step-by-step explanation:
Given: The length of the motorcycle is 7.5 feet.
To find: The size of the cover of motorcycle.
The length of the motorcycle is 7.5 feet. But the covers are only sold in whole foot increments.
So, Juanita should buy 8 feet long cover for motorcycle.
(3x+23x +32) = (x+6)
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Answer:
x = -26/25
Step-by-step explanation:
(3x+23x +32) = (x+6)
Combine like terms
26x +32 = (x+6)
Subtract x from each side
26x -x +32 = x+6-x
25x +32 = 6
Subtract 32 from each side
25x+32 -32 = 6-32
25x = -26
Divide each side by 25
25x/25 = 26/25
x = -26/25
can some one help me solve this −5(p+5over3 )=−4
Answers
Answer:
I did this in my head so I'm not sure but I think it's -1/5=p
Solve the system of equations -30 + 7y = -18 and 4x – 4y = 8 by combining
the equations.
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good luck!
Find the value of 17.64
Answers
Answer:
4.2
Step-by-step explanation:
10. Use substitution to solve the system of equations below.
- x + 2y = 5
3x - 5y =-11
Answers
Answer:
the answer for y is 4 and x is 3
y=4
x=3
Please do this if multiple people answer I will give the best one brainliest
Answers
-7 and 3
-3 and -1
A park volunteer plans to work on the park's stone walls for 1 hour every Monday, 1 hour every
Wednesday, and 3 hours on Fridays. The graph shows the number of hours he plans to work for a
given number of weeks. Complete parts a through c.
Answers
Answer:
The answer is below
Step-by-step explanation:
A linear graph has an equation in the form y = mx + b, where y and x are variables, m is the slope of the line and b is the y intercept (that is value of y at x = 0).
a) y represent the number of hours worked and x represent the number of weeks. The points are represented in the form (x, y).
First we can find the slope of the line by picking two points from the graph. Let us use (0, 0) and (2, 10). The slope m is given as:
[tex]m=\frac{y_2-y_1}{x_2-x_1}\\\\m=\frac{10-0}{2-0} \\\\m=5[/tex]
The slope and constant of proportionality is 5.
b) The equation can be gotten using the points (0, 0) and (2, 10). Therefore:
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)\\\\y-0=\frac{10-0}{2-0}(x-0)\\\\y=5x\\\\[/tex]
c) In 16 weeks (i.e. x = 16):
y = 5x
y = 5(16)
y = 80 hours
Identify the translations of the graph of the parent function f(x) = x^2? that result in the graph of g(x) = (x + 2)2 + 6.
Answers
Answer:
x8
Step-by-step explanation: bacause if you see and look really close
The translations of the graph of the parent function [tex]f(x) = x^2[/tex] that result in the graph of [tex]g(x) = (x + 2)^2 + 6[/tex] will be that the parabola moved [tex]2[/tex] units to the left and [tex]6[/tex] units up.
What is translations ?Translation is the act or process of changing completely. In this also the graph changes or transform. i.e. in the graph values of the expression are changing and forming new shape.
We have,
Parent Quadratic equation [tex]f(x) = x^2[/tex]
And,
Translation of graph [tex]g(x) = (x + 2)^2 + 6[/tex]
So,
Parent quadratic function works in the form of [tex]f(x) = a(x-h)^2 + k[/tex]
Here,
"h" tells if the vertex of the parabola is going left or right.
"k" determines if the vertex of the parabola is going up or down.
So, According to the question;
We have,
Translation of graph [tex]g(x) = (x + 2)^2 + 6[/tex]
So,
From equation we find out that the vertex of the parabola moved [tex]2[/tex] units to the left and [tex]6[/tex] units up.
(Always remember if moving left means sign would be of plus because in parent quadratic function is in the form of [tex]f(x) = a(x-h)^2 + k[/tex] we have minus sign in it.)
Hence, we can say that the Translation of the graph of the parent function [tex]f(x) = x^2[/tex] that result in the graph of [tex]g(x) = (x + 2)^2 + 6[/tex] will be that the parabola moved [tex]2[/tex] units to the left and [tex]6[/tex] units up.
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what is the unit price of $5.36 for 20 oz?
Answers
Answer:
5.36/20
0.268 dollars per oz
plz brainliest :)
do you want an explanation?
What is 287.7 round to the nearest hundredth
Answers
Answer:
287.70 because if u round to the nearest hundreds all u would have to do is add a zero.
I think it's 287.70
A must-have for any thrill seeker is a drop tower ride. The Precipice Plummet will stand 420 feet tall. The scale in your architectural diagrams is 1":40'. How tall will your drawing of Precipice Plummet be in inches? (do not include units in your answer, just the number
Answers
The answer is 10.5, but don't put 10.5 if it's just asking for the number and not the unit only put (10)!!!
Which is an equation of the line with a slope of 4 and a y-intercept of -2?
Answers
Answer:
y = 4x - 2
Step-by-step explanation:
Y-intercepts cross the y-axis at x = 0. So, we can plug (0 , -2) into an equation with m = 4.
-2 = 4(0) + b
-2 = b
y = 4x - 2
John called a plumber to fix a leak in his bathroom. The
plumber charged $30 to come to the house and $25 an hour
while fixing the leak. If the final bill was $105, how many
hours was the plumber at John's house?
Answers
Answer:
3 hours
Step-by-step explanation:
$105 - $30 = $75
$75 ÷ $25 = 3 hours
X(x+7)=0 solve whatever this id
Answers
Step-by-step explanation:
x(x + 7) = 0
By Zero Product rule,
either x = 0 or (x + 7) = 0.
=> x = 0 or x = -7.
90% OFF original price!
Eric wants to buy a chandelier. The original price is $90. What is the sale price?
$
Answers
90% of $90 is $81, so therefore the sale price (original price - percentage) would be $9.
Please help me with this problem, I'll give brainliest!!
And if you want even more points can you go to my profile, then go to QUESTIONS then if you know the answer to the one underneath this one could you help answer it THANK YOU SO MUCH
Answers
In A ABC, m ZA = 36°, m ZB = 45°, and m ZC = 99º. Which statement
is true?
A. CA > BC > AB
B. BC > CA > AB
C. AB > BC > CA
D. AB > CA > BC
Answers
Answer:
The true statement is AB > CA > BC ⇒ D
Step-by-step explanation:
In any triangle, the longest side in length is the opposite to the greatest angle in the measure, and the shortest side in length is opposite to the smallest angle in the measure.
Let us solve the question
∵ ABC is a triangle
∵ m∠A = 36°
∵ m∠B = 45°
∵ m∠C = 99°
→ That means C is the greatest angle and A is the smallest angle
∴ ∠C is the greatest angle and ∠A is the smallest angle
∴ The arrange of the measures of the angles is m∠C > m∠B > m∠A
∵ AB is the opposite side of ∠C
∴ AB is the longest side
∵ BC is the opposite side of ∠A
∴ BC is the shortest side
∵ CA is the opposite side of ∠B
∴ The arrange of the lengths of the sides is AB > CA > BC
∴ The true statement is AB > CA > BC
What is 3/8 +5/12? I need help :>
Answers
Answer:
19/24
Step-by-step explanation:
3/8+5/12
3*3/8*3+5*2/12*2
9/24+10/24
9+10/24
19/24
What is slope? Check all that apply.
Answers
Answer:
B, E, and F maybe
3 multiplied by what gives me 55.50
Answers
Answer:
18.5
Step-by-step explanation:
Divide 55.5 by 3 (working backwards to find your answer)
Then you will get 18.5!
Answer:
18.5
Step-by-step explanation:
divide 55.5 by 3 and you get 18.5.
pls help me for brainlest ASAP
Answers
The slope is 0
Because its not going up, the slope isn’t negative or positive so its moving but it isn’t rising so its 0. If it were going up but not side there would be no slope, but for this its 0
Question 7 Elijah is planning a circular flower garden with a 12 foot diameter. He will put plastic edging along the flowerbed. How many feet of edging will Elijah need to enclose his flower garden? Round to the nearest tenth place. (Use 3.14 for pi)
If you don't know please don't try and help.
Answers
Answer:
37.7 ft
Step-by-step explanation:
c=πd (circumference= 3.14*diameter)
c=3.14*12
c=37.68 ft
rounded to tenths place-37.7 ft
What is the slop in the graph?
Answers
Answer:
-2/5
Step-by-step explanation:
rise/run you count how much it rises and how much it runs
Answer:
-2/5
Step-by-step explanation:
rise over run
PLEASE HURRY WILL GIVE BRAINLIEST TO FASTES PERSON
Answers
Answer:
First is True Second is False Third is True Fourth is False and the last one is False
Step-by-step explanation:
Please give Brainliest
simplify 4a X 6b -3c
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24 abx - 3c
helpppppp it’s urgenttttttttt!!!!!
Answers
A runner has a mass of 89 kg he produces aforce of 84 Newtons between the ground and his running shoes How fast does he accelerate
Answers
Force = mass × acceleration
acc= force / mass
84N/89kg
= 0.94m/s
The acceleration of the runner is 0.9 m/[tex]s^{2}[/tex].
We have a runner has a mass of 89 kg he produces a force of 84 Newtons between the ground and his running shoes.
We have to determine the acceleration of the runner.
What is the formula to calculate the force on a body ?The force on a body is the product of mass and acceleration. Mathematically -
F = ma
According to the question, we have -
Force = 84 N
Mass = 89 Kg
Therefore -
F = ma
84 = 89 x a
a = 84/89 = 0.9 m/[tex]s^{2}[/tex]
Hence, the acceleration of the runner is 0.9 m/[tex]s^{2}[/tex].
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A football coach moves 12 m north, then 16 m south, then 22 m north, and finally 6 m
south.
What is the displacement
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Answer: Displacement=12 m north
Step-by-step explanation:
12 m north
Let’s assume
north= positive
south=negative
12+(-16)+22+(-6)=12