Question:
Which equation does the graph of the systems of equations solve
?
Option A:−1/3x + 3 = x − 1
Option B: 1/3x − 3 = −x + 1
Option C: −1/3x + 3 = −x − 1
Option D: 1/3x + 3 = x − 1
Answer:
Option B: ![\frac{1}{3}x-3=-x+1](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B3%7Dx-3%3D-x%2B1)
Solution:
Option A: ![\frac{-1}{3}x+3=x-1](https://tex.z-dn.net/?f=%5Cfrac%7B-1%7D%7B3%7Dx%2B3%3Dx-1)
Add 1 on both sides of the equation.
![\frac{-1}{3}x+4=x](https://tex.z-dn.net/?f=%5Cfrac%7B-1%7D%7B3%7Dx%2B4%3Dx)
Add
on both sides of the equation.
![4=\frac{4}{3}x](https://tex.z-dn.net/?f=4%3D%5Cfrac%7B4%7D%7B3%7Dx)
Multiply by 3 on both sides.
12 = 4x
Divide by 4.
x = 3
Substitute this in x – 1, we get
y = 3 – 1 = 2
(3, 2) is not a solution.
Option B: ![\frac{1}{3}x-3=-x+1](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B3%7Dx-3%3D-x%2B1)
Add 3 on both sides of the equation.
![\frac{1}{3}x=-x+4](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B3%7Dx%3D-x%2B4)
Add x on both sides of the equation.
![\frac{4}{3}x=4](https://tex.z-dn.net/?f=%5Cfrac%7B4%7D%7B3%7Dx%3D4)
Divide by 4.
x = 3
Substitute this in –x + 1, we get
y = –3 + 1 = –2
(3, –2) is a solution.
Option C: ![\frac{-1}{3}x+3=-x-1](https://tex.z-dn.net/?f=%5Cfrac%7B-1%7D%7B3%7Dx%2B3%3D-x-1)
Subtract 3 on both sides of the equation.
![\frac{1}{3}x=-x-4](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B3%7Dx%3D-x-4)
Add x on both sides of the equation.
![\frac{4}{3}x=-4](https://tex.z-dn.net/?f=%5Cfrac%7B4%7D%7B3%7Dx%3D-4)
Divide by 4.
x = –3
Substitute this in –x – 1, we get
y = –3 – 1 = –4
(3, –4) is not a solution.
Option D: ![\frac{1}{3}x+3=x-1](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B3%7Dx%2B3%3Dx-1)
Add 1 on both sides of the equation.
![\frac{1}{3}x+4=x](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B3%7Dx%2B4%3Dx)
Subtract
on both sides of the equation.
![4=\frac{2}{3}x](https://tex.z-dn.net/?f=4%3D%5Cfrac%7B2%7D%7B3%7Dx)
Multiply by 3 on both sides.
12 = 2x
Divide by 2.
x = 6
Substitute this in x – 1, we get
y = 6 – 1 = 5
(6, 5) is not a solution.
Hence Option B is the correct answer.
The equation of the graph of the system of equations is
.