Question

Which equation does the graph of the systems of equations solve? On the graph there is two linear functions intersecting at 2, 2

answer options:
a.−1/2x + 3 = 3x − 4
b. −1/2x − 3 = −3x + 4
c. 1/2x + 3 = 3x + 4
d. 1/2x + 3 = −3x − 4

Answer 1

The answer is "a. -1/2x + 3 = 3x − 4".
Just plug 2 in for x for each expression, and when both expressions in an answer choice's equation are equal to 2 (when x = 2), you have your answer.
The answer is "a. -1/2x + 3 = 3x − 4".

Answer 2

The equation which the graph of the system of equation solve is:

Option: a
`(-1)/(2)x+3=3x-4`

Explanation:

It is given that:

On the graph there is two linear functions intersecting at (2, 2 )

This means that both the equations i.e. the equation on left and right hand side of the equality must pass through (2,2)

i.e. when x=2 the value of the expression must be 2.

b)

`(-1)/(2)x-3=-3x+4`

on taking left hand side

`(-1)/(2)x-3`

when x=2 we get:

`=(-1)/(2)* 2-3\\\\\\=-1-3\\\\\\=-4\\eq 2`

Hence, option: b is incorrect.

c)

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

on taking left hand side

`(1)/(2)x+3`

when x=2 we get:

`=(1)/(2)* 2+3\\\\\\=1+3\\\\\\=4\\eq 2`

Hence, option: c is incorrect.

d)

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

on taking left hand side

`(1)/(2)x+3`

when x=2 we get:

`=(1)/(2)* 2+3\\\\\\=1+3\\\\\\=4\\eq 2`

Hence, option: d is incorrect.

Hence, we are left with option: a

a)

`(-1)/(2)x+3=3x-4`

on taking left hand side

`(-1)/(2)x+3`

when x=2 we have:

`=(-1)/(2)* 2+3\\\\\\=-1+3\\\\\\=2`

Also, on taking the right hand side

`3x-4`

when x=2 we have:

`=3* 2-4\\\\\\=6-4\\\\\\=2`

Hence, it passes through (2,2)