Question

determine which of the ordered pairs are solutions to the given system of equations. system: \\(\

$$\begin{cases} y = \\frac{1}{2}x - 4 \\\\ 2x - 4y = 16 \\end{cases}$$

\\), ordered pairs: \\((4, -2), (-2, -5)\\). select one: \\(\circ\\) a. neither pair is the solution. \\(\circ\\) b. only pair \\((-2, -5)\\) is the solution. \\(\circ\\) c. both pairs are the solution. \\(\circ\\) d. only pair \\((4, -2)\\) is the solution.

Explanation:

Step1: Test pair (4, -2) in first equation

Substitute $x=4, y=-2$ into $y=\frac{1}{2}x-4$:
$\frac{1}{2}(4)-4 = 2-4=-2$, which equals $y$.

Step2: Test pair (4, -2) in second equation

Substitute $x=4, y=-2$ into $2x-4y=16$:
$2(4)-4(-2)=8+8=16$, which matches the right-hand side.

Step3: Test pair (-2, -5) in first equation

Substitute $x=-2, y=-5$ into $y=\frac{1}{2}x-4$:
$\frac{1}{2}(-2)-4=-1-4=-5$, which equals $y$.

Step4: Test pair (-2, -5) in second equation

Substitute $x=-2, y=-5$ into $2x-4y=16$:
$2(-2)-4(-5)=-4+20=16$, which matches the right-hand side.

Answer:

C. Both pairs are the solution.