Question

Solve the system of equations using the linear combination method.

{4x−3y=12 7x−3y=3

Answer 1

To solve the system of equations using the linear combination method, we start with the given equations:

1. \( 4x - 3y = 12 \) (Equation 1)
2. \( 7x - 3y = 3 \) (Equation 2)

Now, we will eliminate one of the variables by subtracting one equation from the other. Since both equations have \(-3y\), we can eliminate \(y\) by subtracting Equation 1 from Equation 2.

Subtract Equation 1 from Equation 2:

\[
(7x - 3y) - (4x - 3y) = 3 - 12
\]

Simplifying the left side:

\[
7x - 3y - 4x + 3y = 3 - 12
\]

This simplifies to:

\[
3x = -9
\]

Now, divide by 3:

\[
x = -3
\]

Next, we will substitute \(x = -3\) back into one of the original equations to find \(y\). We can use Equation 1:

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

This simplifies to:

\[
-12 - 3y = 12
\]

Add 12 to both sides:

\[
-3y = 12 + 12
\]
\[
-3y = 24
\]

Now, divide by -3:

\[
y = -8
\]

Thus, the solution to the system of equations is:

\[
\boxed{(-3, -8)}
\]