Question

use the system of equations below to answer the question$\begin{cases} y = -\frac{1}{2}x - 1 \\ y = 2x - 16 end{cases}$8what is the solution to the system?a $(-1,-4)$b $(16,2)$c no solutiond $(6,-4)$

Explanation:

Step1: Set equations equal

Since both equal $y$, set them equal:
$$-\frac{1}{2}x - 1 = 2x - 16$$

Step2: Multiply to eliminate fraction

Multiply all terms by 2:
$$-x - 2 = 4x - 32$$

Step3: Isolate $x$ terms

Move $x$ terms to left, constants to right:
$$-x - 4x = -32 + 2$$
$$-5x = -30$$

Step4: Solve for $x$

Divide both sides by $-5$:
$$x = \frac{-30}{-5} = 6$$

Step5: Find $y$ with $x=6$

Substitute $x=6$ into $y=2x-16$:
$$y = 2(6) - 16 = 12 - 16 = -4$$

Answer:

D. (6, -4)