Question

To solve by elimination, state what the first step would be in order to eliminate the
-term in the following system of equations
-3x-5y=15
2x-5y=10

Answer 1

To eliminate the \(-5y\) term from the system of equations:

1. **Identify the equations:**
\[
\text{Equation 1: } -3x - 5y = 15
\]
\[
\text{Equation 2: } 2x - 5y = 10
\]

2. **Notice that both equations already have the \(-5y\) term.** To eliminate the \(-5y\) term, we can subtract Equation 2 from Equation 1, or vice versa, since the coefficients of \(y\) in both equations are the same.

3. **First step: Subtract Equation 2 from Equation 1:**
\[
(-3x - 5y) - (2x - 5y) = 15 - 10
\]

This will allow you to eliminate the \(y\) variable and solve for \(x\).

So, the first step to eliminate \(-5y\) is to subtract the second equation from the first.