To determine which ordered pair is the solution to the given system of equations:
[tex]\[
\begin{cases}
-3x + 4y = -20 \\
y = x - 4
\end{cases}
\][/tex]
we need to check each provided point (ordered pair) to see if it satisfies both equations.
Let's go through each point step by step.
1. Point [tex]\((-2, -6)\)[/tex]:
- Substitute [tex]\(x = -2\)[/tex] and [tex]\(y = -6\)[/tex] into the equations:
[tex]\[
-3(-2) + 4(-6) = -20
\][/tex]
[tex]\[
6 - 24 = -20 \quad (satisfied)
\][/tex]
[tex]\[
-6 = -2 - 4
\][/tex]
[tex]\[
-6 = -6 \quad (satisfied)
\][/tex]
- Point [tex]\((-2, -6)\)[/tex] satisfies both equations.
2. Point [tex]\((-4, -8)\)[/tex]:
- Substitute [tex]\(x = -4\)[/tex] and [tex]\(y = -8\)[/tex] into the equations:
[tex]\[
-3(-4) + 4(-8) = -20
\][/tex]
[tex]\[
12 - 32 = -20 \quad (satisfied)
\][/tex]
[tex]\[
-8 = -4 - 4
\][/tex]
[tex]\[
-8 = -8 \quad (satisfied)
\][/tex]
- Point [tex]\((-4, -8)\)[/tex] satisfies both equations.
3. Point [tex]\((4, 8)\)[/tex]:
- Substitute [tex]\(x = 4\)[/tex] and [tex]\(y = 8\)[/tex] into the equations:
[tex]\[
-3(4) + 4(8) = -20
\][/tex]
[tex]\[
-12 + 32 = 20 \quad (not satisfied)
\][/tex]
- Point [tex]\((4, 8)\)[/tex] does not satisfy the first equation and hence is not a solution.
4. Point [tex]\((0, -5)\)[/tex]:
- Substitute [tex]\(x = 0\)[/tex] and [tex]\(y = -5\)[/tex] into the equations:
[tex]\[
-3(0) + 4(-5) = -20
\][/tex]
[tex]\[
0 - 20 = -20 \quad (satisfied)
\][/tex]
[tex]\[
-5 = 0 - 4
\][/tex]
[tex]\[
-5 \neq -4 \quad (not satisfied)
\][/tex]
- Point [tex]\((0, -5)\)[/tex] does not satisfy the second equation and hence is not a solution.
After checking all the points, the solution to the system of equations is:
[tex]\[\boxed{(-4, -8)}\][/tex]
