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 (, ).

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

Substitute $y=2x+2$ into simplified equation:
$$2x + 2 = -x - 10$$

Step3: Solve for $x$

Combine like terms and isolate $x$:
$$2x + x = -10 - 2 \implies 3x = -12 \implies x = \frac{-12}{3} = -4$$

Step4: Solve for $y$

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

Answer:

$(-4, -6)$