Question

Finish solving the system of equations –9.5x – 2.5y = –4.3 and 7x + 2.5y = 0.8 using the linear combination method.

1. Determine which variable will be eliminated:  y will be eliminated because –2.5y and 2.5y are opposite terms.

2. Add the equations together to create a one-variable linear equation:   –2.5x = –3.5

3. Solve to determine the unknown variable in the equation:        x = 1.4

4. Substitute the value of the variable into either original equation to solve for the other variable.

The solution to the system is (
,
).

Answer 1

Let's complete the solution by following the steps you have outlined:

1. You decided to eliminate \(y\), and you are correct since \(-2.5y\) and \(2.5y\) are opposites.

2. Now, add the equations together:

\[
-9.5x - 2.5y + 7x + 2.5y = -4.3 + 0.8
\]

The \(y\) terms cancel out:

\[
(-9.5x + 7x) = -4.3 + 0.8
\]

\[
-2.5x = -3.5
\]

3. Now, solve for \(x\):

\[
x = \frac{-3.5}{-2.5} = \frac{3.5}{2.5} = 1.4
\]

4. Substitute \(x = 1.4\) into one of the original equations to solve for \(y\). Let's use the second equation:

\[
7x + 2.5y = 0.8
\]

Substituting \(x = 1.4\):

\[
7(1.4) + 2.5y = 0.8
\]

Calculate \(7(1.4)\):

\[
9.8 + 2.5y = 0.8
\]

Now, isolate \(2.5y\):

\[
2.5y = 0.8 - 9.8
\]
\[
2.5y = -9.0
\]

Now, solve for \(y\):

\[
y = \frac{-9.0}{2.5} = -3.6
\]

So, the solution to the system of equations is:

\[
\boxed{(1.4, -3.6)}
\]