Question

Solving systems by elimination 6x-6y=0 -7x+10y=-9

Answer 1

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

1) \( 6x - 6y = 0 \)

2) \( -7x + 10y = -9 \)

First, we can simplify equation (1). Dividing the entire equation by 6:

\[
x - y = 0 \quad \Rightarrow \quad x = y
\]

Now, we substitute \( x = y \) into equation (2):

\[
-7(y) + 10y = -9
\]

This simplifies to:

\[
-7y + 10y = -9
\]

Combining like terms gives:

\[
3y = -9
\]

Now, divide by 3:

\[
y = -3
\]

Now that we have \( y \), we use it to find \( x \):

\[
x = y = -3
\]

So the solution to the system of equations is:

\[
x = -3, \quad y = -3
\]

The solution can be presented as the ordered pair:

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