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: [tex]\frac{1}{3}x-3=-x+1[/tex]
Solution:
Option A: [tex]\frac{-1}{3}x+3=x-1[/tex]
Add 1 on both sides of the equation.
[tex]\frac{-1}{3}x+4=x[/tex]
Add [tex]\frac{1}{3}x[/tex] on both sides of the equation.
[tex]4=\frac{4}{3}x[/tex]
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: [tex]\frac{1}{3}x-3=-x+1[/tex]
Add 3 on both sides of the equation.
[tex]\frac{1}{3}x=-x+4[/tex]
Add x on both sides of the equation.
[tex]\frac{4}{3}x=4[/tex]
Divide by 4.
x = 3
Substitute this in –x + 1, we get
y = –3 + 1 = –2
(3, –2) is a solution.
Option C: [tex]\frac{-1}{3}x+3=-x-1[/tex]
Subtract 3 on both sides of the equation.
[tex]\frac{1}{3}x=-x-4[/tex]
Add x on both sides of the equation.
[tex]\frac{4}{3}x=-4[/tex]
Divide by 4.
x = –3
Substitute this in –x – 1, we get
y = –3 – 1 = –4
(3, –4) is not a solution.
Option D: [tex]\frac{1}{3}x+3=x-1[/tex]
Add 1 on both sides of the equation.
[tex]\frac{1}{3}x+4=x[/tex]
Subtract [tex]\frac{1}{3}x[/tex] on both sides of the equation.
[tex]4=\frac{2}{3}x[/tex]
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 [tex]\frac{1}{3}x-3=-x+1[/tex].
