Question

Which equation does the graph of the systems of equations solve? 2 linear graphs. They intersect at 0,3

−2x + 3 = 8x − 3

−2x + 4 = −8x + 4

2x + 4 = 8x − 4

2x + 3 = −8x + 3

Answer 1

D.
`2x+3=-8x+3`

Explanation:

We have been given a graph of system of linear equations and we are asked to choose the system of equations representing the given graph.

Upon looking at our graph we can see that our lines intersect at point (0,3). To find the system of equations represented in the graph we will substitute x=0 in our given equations and see which equation gives us an output of 3.

Let us start with 1st option.

A.
`-2x+3=8x-3`

Upon substituting x=0 we will get

`-2*0+3=8*0-3`

`0+3=0-3`

`3\\eq-3`

Since we get 3 on one side of equation and -3 on other side of equation, therefore, option A is not a correct choice.

B.
`-2x+4=-8x+4`

Upon substituting x=0 we will get,

`-2*0+4=-8*0+4`

`0+4=0+4`

`4=4`

Since this system of equations intersect at point (0,4), therefore, option B is not a correct choice as well.

C.
`2x+4=8x-4`

Upon substituting x=0 we will get,

`2*0+4=8*0-4`

`0+4=0-4`

`4\\eq-4`

Therefore, option C is not a correct choice as well.

D.
`2x+3=-8x+3`

Upon substituting x=0 we will get,

`2*0+3=-8*0+3`

`0+3=0+3`

`3=3`

Since this system of equations intersect at point (0,3), therefore, option D is the correct choice.