Question

The system of linear equations 3x + 2y = −4 and y equals one half times x plus 1 is graphed on a coordinate plane. Approximate the solution to the system.

coordinate plane with one line that passes through the points 0 comma negative 2 and negative 2 comma 1 and another line that passes through the points 0 comma 1 and 2 comma 2

(−1.5, 0.25)
(−0.5, 0.75)
(1.5, 0.25)
(−2.5, 1.5)

Answer 1

To approximate the solution to the system of equations, we need to find the point where the two lines intersect. From the second equation, we know that y = (1/2)x + 1. Substituting this expression for y into the first equation gives:

3x + 2[(1/2)x + 1] = -4

Simplifying and solving for x, we get:

3x + x + 2 = -4

4x = -6

x = -1.5

Substituting this value of x back into the second equation gives:

y = (1/2)(-1.5) + 1 = 0.25

Therefore, the solution to the system of equations is approximately (-1.5, 0.25).

So the answer is (−1.5, 0.25).