Question

Which equation does the graph of the systems of equations solve?

2 linear graphs. They intersect at 1,2

x + 4 = −2x − 1
x + 2 = −3x + 1
−x + 3 = 3x − 1
x + 3 = 2x − 1

Answer 1

The correct option is 3.

Explanation:

It is given that two linear graphs intersect at (1,2). It means the solution of both lines is x=1 and y=2.

The equation which is satisfied by x=1 will be the required equation.

In option (1),

`x+4=-2x-1`

Substitute x=1.

`(1)+4=-2(1)-1`

`5\\eq -3`

Option 1 is incorrect.

In option (2),

`x+2=-3x+1`

Substitute x=1.

`(1)+2=-3(1)+1`

`3\\eq -2`

Option 2 is incorrect.

In option (3),

`-x+3=3x-1`

Substitute x=1.

`-(1)+3=3(1)-1`

`2=2`

Option 3 is correct.

In option (1),

`x+3=2x-1`

Substitute x=1.

`(1)+3=2(1)-1`

`4\\eq 1`

Option 4 is incorrect.

Therefore the correct option is 3.

Answer 2

We substitute the point of intesection (1, 2) into the given options to see that only -x + 3 = 3x - 1 satisfies the graphs.
i.e. -x + 3 = -1 + 3 = 2
3x - 1 = 3(1) - 1 = 3 - 1 = 2.