Question

From the options below, choose the first step to eliminate x in order to solve the following system of equations using elimination.

10x-2y=-20
10x-60y=240

Group of answer choices

Multiply the top equation by -30

Multiply the one of the equations by -1

Just add them together immediately

Multiply the bottom equation by 12

Answer 1

To eliminate \(x\) in the system of equations, we want to manipulate the equations so that the coefficients of \(x\) in both equations are opposites.

Given the equations:

1. \(10x - 2y = -20\)
2. \(10x - 60y = 240\)

Both equations already have the same coefficient for \(x\) (which is 10). Therefore, we can eliminate \(x\) by making one coefficient negative.

Among the options given:

1. **Multiply the top equation by -30**: This would change the 10x to -300x, which is not helpful for elimination.
2. **Multiply one of the equations by -1**: This would change one of the \(10x\) terms to \(-10x\), allowing us to eliminate \(x\) when we add the two equations.
3. **Just add them together immediately**: This would not eliminate \(x\), as both would remain \(10x\).
4. **Multiply the bottom equation by 12**: This would increase the equation's complexity and does not help in eliminating \(x\).

The best first step to eliminate \(x\) is:

**Multiply one of the equations by -1**.

This will give the desired result for elimination.