Which graph represents the solution set to this system of equations? y = - 1 2 x + 3 and y = 1 2 x - 1 On a coordinate plane, a line goes through (negative 4, 1) and (0, 3) and another line goes through (negative 2, negative 2) and (0, negative 1). On a coordinate plane, a line goes through (negative 2, 2) and (0, 3) and another line goes through (negative 2, 0) and (0, negative 1). On a coordinate plane, a line goes through (negative 2, 0) and (0, negative 1). On a coordinate plane, a line goes through (0, 3) and (2, 2) and another line goes through (0, negative 1) and (2, 0).

It's C

I got it wrong and it showed me the right answer (which is C)

On a coordinate plane, a line goes through (0, 3) and (2, 2) and another line goes through (0, negative 1) and (2, 0).

Step-by-step explanation:

Given that the system of equations are:

y = - 1 / 2 x + 3 and y = 1 / 2 x - 1

Let us first try the first option

On a coordinate plane, a line goes through ( - 4, 1) and (0, 3) and another line goes through (-2, - 2) and (0, - 1)

The slope M1 = (3-1) / (0--4) = 2/4 = 1/2

The calculated slope is positive. But the slope of the first equation is negative. So we ignore the first option.

The next option that makes sense is the last option. That is

On a coordinate plane, a line goes through (0, 3) and (2, 2) and another line goes through (0, - 1) and (2, 0). So let also try it by calculating the two slopes

M1 = (2-3) / (2-0) = - 1/2 (perfect)

M2 = (0 - - 1) / (2-0) = 1/2 (perfect)

Because, from the two equations

y = - 1 / 2 x + 3 and y = 1 / 2 x - 1

The slope of the first is negative and the slope of the second is positive. Also, they have a corresponding intercept which are positive 3 and negative 1