Question

practice analyzing a system of linear equations with one solution. graph the system of linear equations. $-\frac{1}{2}y = \frac{1}{2}x + 5$ and $y = 2x + 2$ the solution to the system is (dropdown, dropdown) with options -6, -4, 4, 6 (graph and table present: click or tap the graph to plot a point)

Explanation:

Step1: Simplify first equation

Multiply both sides by -2:
$$-\frac{1}{2}y = \frac{1}{2}x + 5 \implies y = -x - 10$$

Step2: Set equations equal

Since both equal $y$, equate them:
$$-x - 10 = 2x + 2$$

Step3: Solve for $x$

Isolate $x$ terms and solve:
$$-10 - 2 = 2x + x \implies -12 = 3x \implies x = \frac{-12}{3} = -4$$

Step4: Find $y$ value

Substitute $x=-4$ into $y=2x+2$:
$$y = 2(-4) + 2 = -8 + 2 = -6$$

Answer:

$(-4, -6)$