Question

Which equation does the graph of the systems of equations solve

Answer 1

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: $\frac{1}{3}x-3=-x+1$

Solution:

Option A: $\frac{-1}{3}x+3=x-1$

Add 1 on both sides of the equation.

$\frac{-1}{3}x+4=x$

Add $\frac{1}{3}x$ on both sides of the equation.

$4=\frac{4}{3}x$

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: $\frac{1}{3}x-3=-x+1$

Add 3 on both sides of the equation.

$\frac{1}{3}x=-x+4$

Add x on both sides of the equation.

$\frac{4}{3}x=4$

Divide by 4.

x = 3

Substitute this in –x + 1, we get

y = –3 + 1 = –2

(3, –2) is a solution.

Option C: $\frac{-1}{3}x+3=-x-1$

Subtract 3 on both sides of the equation.

$\frac{1}{3}x=-x-4$

Add x on both sides of the equation.

$\frac{4}{3}x=-4$

Divide by 4.

x = –3

Substitute this in –x – 1, we get

y = –3 – 1 = –4

(3, –4) is not a solution.

Option D: $\frac{1}{3}x+3=x-1$

Add 1 on both sides of the equation.

$\frac{1}{3}x+4=x$

Subtract $\frac{1}{3}x$ on both sides of the equation.

$4=\frac{2}{3}x$

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 $\frac{1}{3}x-3=-x+1$.