Question

y = -\frac{1}{2}x - 6\
y = \frac{3}{2}x + 2

Explanation:

Step1: Set equations equal

Since $y$ is equal to both expressions, set them equal to each other:
$$-\frac{1}{2}x - 6 = \frac{3}{2}x + 2$$

Step2: Eliminate fractions

Multiply all terms by 2 to eliminate denominators:
$$-x - 12 = 3x + 4$$

Step3: Isolate x terms

Bring $x$ terms to one side and constants to the other:
$$-x - 3x = 4 + 12$$
$$-4x = 16$$

Step4: Solve for x

Divide both sides by -4:
$$x = \frac{16}{-4} = -4$$

Step5: Solve for y

Substitute $x=-4$ into $y=\frac{3}{2}x + 2$:
$$y = \frac{3}{2}(-4) + 2 = -6 + 2 = -4$$

Answer:

The solution to the system is $x=-4$, $y=-4$, or the point $(-4, -4)$