Question

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

two linear functions intersecting at 2, 2

−one halfx + 3 = 3x − 4
−one halfx − 3 = −3x + 4
one halfx + 3 = 3x + 4
one halfx + 3 = −3x − 4

Answer 1

To determine which equation the graph of the system of equations solves, we need to solve the system of equations and see which equation represents the graph at the point of intersection.

The system of equations can be written as:

-1/2x + 3 = 3x - 4

-1/2x - 3 = -3x + 4

We can simplify the first equation by adding 1/2x and 4 to both sides:

3.5x = 7

x = 2

Substituting x = 2 into the second equation:

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

-1 - 3 = -6 + 4

-4 = -2

Since -4 does not equal -2, we know that there is no solution to this system of equations. Therefore, the graph of the system of equations does not solve any of the given equations.