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.

Answer 1

To solve the system of equations using the substitution method, we first need to isolate one of the variables in one of the equations. Let's use the first equation to express \(y\) in terms of \(x\).

Given the equations:

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

From the first equation, we can isolate \(y\):

\[
y = 6 + 4x
\]

Now we will substitute this expression for \(y\) into the second equation. The second equation can be rewritten as:

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

Now simplify this:

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

Next, add 6 to both sides:

\[
-9x = 27
\]

Now, divide both sides by -9:

\[
x = -3
\]

Now that we have the value of \(x\), we can substitute it back into the expression we found for \(y\):

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

Thus, the solution to the system of equations is:

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

Please fill in the boxes:

\(x = -3\)

\(y = -6\)