Question

or
Solve using elimination.

3x − 5y = 15
–x + 5y = 5

Answer 1

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

1. \(3x - 5y = 15\) (Equation 1)
2. \(-x + 5y = 5\) (Equation 2)

We can eliminate \(y\) by adding both equations. To do this, it’s helpful to align the coefficients of \(y\). We can manipulate Equation 2:

First, we'll add Equation 1 and Equation 2:

\[
3x - 5y + (-x + 5y) = 15 + 5
\]

This simplifies to:

\[
(3x - x) + (-5y + 5y) = 20
\]

\[
2x + 0 = 20
\]

This results in:

\[
2x = 20
\]

Now we'll solve for \(x\):

\[
x = \frac{20}{2} = 10
\]

Next, we will substitute \(x = 10\) back into either original equation to find \(y\). Let's use Equation 2 for that:

\[
-x + 5y = 5
\]

Substituting \(x\):

\[
-10 + 5y = 5
\]

\[
5y = 5 + 10
\]

\[
5y = 15
\]

Now solve for \(y\):

\[
y = \frac{15}{5} = 3
\]

So, the solution to the system of equations is:

\[
x = 10, \quad y = 3
\]

In coordinate form, the solution is \((10, 3)\).