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:
`(1)/(3)x-3=-x+1`

Solution:

Option A:
`(-1)/(3)x+3=x-1`

Add 1 on both sides of the equation.

`(-1)/(3)x+4=x`

Add
`(1)/(3)x` on both sides of the equation.

`4=(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:
`(1)/(3)x-3=-x+1`

Add 3 on both sides of the equation.

`(1)/(3)x=-x+4`

Add x on both sides of the equation.

`(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:
`(-1)/(3)x+3=-x-1`

Subtract 3 on both sides of the equation.

`(1)/(3)x=-x-4`

Add x on both sides of the equation.

`(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:
`(1)/(3)x+3=x-1`

Add 1 on both sides of the equation.

`(1)/(3)x+4=x`

Subtract
`(1)/(3)x` on both sides of the equation.

`4=(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
`(1)/(3)x-3=-x+1`.