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

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.

Answer 2

Answer:

The correct option is 3.

Step-by-step 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.

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

$5\neq -3$

Option 1 is incorrect.

In option (2),

$x+2=-3x+1$

Substitute x=1.

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

$3\neq -2$

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.

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

$4\neq 1$

Option 4 is incorrect.

Therefore the correct option is 3.