Question

What is the solution to the system of equations?

Use the substitution method to solve.

6=−4x+y−5x−y=21

Enter your answer by filling in the boxes.

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Answer 1

To solve the system of equations using the substitution method, let's first rewrite the equations clearly. The equations appear to be:

1. \( 6 = -4x + y \)
2. \(-5x - y = 21 \)

First, we can solve for \( y \) from the first equation:

\[
y = 6 + 4x
\]

Next, we substitute this expression for \( y \) into the second equation:

\[
-5x - (6 + 4x) = 21
\]

Now, we simplify this equation:

\[
-5x - 6 - 4x = 21
\]
\[
-9x - 6 = 21
\]

Next, we add 6 to both sides:

\[
-9x = 21 + 6
\]
\[
-9x = 27
\]

Now, we divide by -9:

\[
x = -3
\]

With \( x \) found, we can substitute this value back into the equation for \( y \):

\[
y = 6 + 4(-3)
\]
\[
y = 6 - 12
\]
\[
y = -6
\]

So, the solution to the system of equations is:

\[
(x, y) = (-3, -6)
\]

Enter your answer as:

\((-3, -6)\)