Which ordered pair is the solution to the system of equations?

[tex]\[
\left\{
\begin{array}{l}
-3x + 4y = -20 \\
y = x - 4
\end{array}
\right.
\][/tex]

A. [tex]\((-2, -6)\)[/tex]

B. [tex]\((-4, -8)\)[/tex]

C. [tex]\((4, 8)\)[/tex]

D. [tex]\((0, -5)\)[/tex]



Answer :

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]