Question

Solve using substitution.

8x + 4y = 4
4x + y = 11

Answer 1

To solve the system of equations using substitution, we first need to express one variable in terms of the other from one of the equations.

We start with the second equation:

\[ 4x + y = 11 \]

We can solve for \( y \):

\[ y = 11 - 4x \]

Now we can substitute this expression for \( y \) into the first equation:

\[ 8x + 4y = 4 \]

Substituting \( y \):

\[ 8x + 4(11 - 4x) = 4 \]

Now, simplify the equation:

\[ 8x + 44 - 16x = 4 \]

Combine like terms:

\[ -8x + 44 = 4 \]

Next, isolate \( x \):

\[ -8x = 4 - 44 \]
\[ -8x = -40 \]

Now, divide by -8:

\[ x = 5 \]

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

\[ y = 11 - 4x \]
\[ y = 11 - 4(5) \]
\[ y = 11 - 20 \]
\[ y = -9 \]

Thus, the solution to the system of equations is:

\[
\boxed{(5, -9)}
\]

**Verification:**

We can verify our solution by substituting \( (5, -9) \) back into the original equations.

1. For the first equation \( 8x + 4y = 4 \):
\[
8(5) + 4(-9) = 40 - 36 = 4 \quad \text{(True)}
\]

2. For the second equation \( 4x + y = 11 \):
\[
4(5) + (-9) = 20 - 9 = 11 \quad \text{(True)}
\]

Both equations are satisfied, confirming that the solution \( (5, -9) \) is correct.