Question

solve the system using elimination. 7) -6x+6y=6
-6x+3y=12

Answer 1

To solve the system of equations using the elimination method, we start with the following equations:

1) \(-6x + 6y = 6\) (Equation 1)
2) \(-6x + 3y = 12\) (Equation 2)

We want to eliminate one of the variables by making the coefficients of \(x\) or \(y\) the same in both equations.

Notice that both equations have the same coefficient for \(x\) (-6). Thus, we can subtract one equation from the other to eliminate \(x\).

Let's subtract Equation 2 from Equation 1:

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

This simplifies to:

\[
6y - 3y = -6
\]

\[
3y = -6
\]

Now, divide both sides by 3:

\[
y = -2
\]

Now we can substitute \(y = -2\) back into one of the original equations to find \(x\). We'll use Equation 1:

\[
-6x + 6(-2) = 6
\]

This simplifies to:

\[
-6x - 12 = 6
\]

Now add 12 to both sides:

\[
-6x = 18
\]

Now divide by -6:

\[
x = -3
\]

Now we have \(x = -3\) and \(y = -2\).

The solution to the system of equations is:
\[
(x, y) = (-3, -2)
\]