Question

Solve using elimination.

10x + 10y = –10
x + 2y = –8

Answer 1

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

1) \( 10x + 10y = -10 \)
2) \( x + 2y = -8 \)

First, we want to eliminate one of the variables. Let's eliminate \( x \). To do that, we can multiply the second equation by \( 10 \) to match the coefficient of \( x \) in the first equation.

Multiplying the second equation by \( 10 \):

\[
10(x + 2y) = 10(-8)
\]

This gives us:

\[
10x + 20y = -80
\]

Now we rewrite our system of equations:

1) \( 10x + 10y = -10 \)
2) \( 10x + 20y = -80 \)

Next, we subtract the first equation from the second equation:

\[
(10x + 20y) - (10x + 10y) = -80 - (-10)
\]

This simplifies to:

\[
10y = -80 + 10
\]

So,

\[
10y = -70
\]

Now divide both sides by \( 10 \):

\[
y = -7
\]

Now that we have the value of \( y \), we can substitute it back into one of the original equations to find \( x \). Let's substitute \( y = -7 \) into the second equation:

\[
x + 2(-7) = -8
\]

Simplifying that:

\[
x - 14 = -8
\]

Next, we add \( 14 \) to both sides:

\[
x = -8 + 14
\]

Thus:

\[
x = 6
\]

Now we have the solution:

\[
x = 6, \quad y = -7
\]

The solution to the system of equations is:

\[
(6, -7)
\]