Question

Solve the linear system of equations using the linear combination method.

{4x−9y=202x−6y=16



Enter your answers in the boxes.

x =

y =

Answer 1

To solve the system of equations using the linear combination method, we first write down the equations:

1. \( 4x - 9y = 20 \) (Equation 1)
2. \( 2x - 6y = 16 \) (Equation 2)

To eliminate one of the variables, we can manipulate these equations. Let's aim to eliminate \( x \).

To do this, we can multiply Equation 2 by 2 so that the coefficients of \( x \) in both equations will match:

\[
2(2x - 6y) = 2(16)
\]

This simplifies to:

\[
4x - 12y = 32 \quad (Equation 3)
\]

Now we have:

1. \( 4x - 9y = 20 \) (Equation 1)
2. \( 4x - 12y = 32 \) (Equation 3)

Next, we will subtract Equation 1 from Equation 3 to eliminate \( x \):

\[
(4x - 12y) - (4x - 9y) = 32 - 20
\]

This simplifies to:

\[
-12y + 9y = 12
\]

\[
-3y = 12
\]

Dividing by \(-3\):

\[
y = -4
\]

With \( y \) found, we substitute \( y = -4 \) back into one of the original equations to find \( x \). We can use Equation 2 for this:

\[
2x - 6(-4) = 16
\]

This simplifies to:

\[
2x + 24 = 16
\]

Subtracting 24 from both sides:

\[
2x = 16 - 24
\]

\[
2x = -8
\]

Dividing by 2:

\[
x = -4
\]

Now we have the values:

\[
x = -4 \quad \text{and} \quad y = -4
\]

Thus, the final answer is:

\[
\begin{align*}
x & = -4 \\
y & = -4
\end{align*}
\]