Question

Consider the system of equations
x-3y=2
4x+7y=27

What could be the first step in solving the system of equations using elimination?

Question 2 options:

Multiply the first equation by 7.


Add the two equations.


Multiply the first equation by -4.


Add the two equations.

Answer 1

To use the elimination method to solve the given system of equations, you want to eliminate one of the variables by making the coefficients of that variable the same (or opposites) in both equations.

The given system is:
1. \( x - 3y = 2 \) (Equation 1)
2. \( 4x + 7y = 27 \) (Equation 2)

To eliminate \( x \) quickly, you could multiply the first equation by -4, which would make the coefficient of \( x \) in Equation 1 equal to -4:

\[
-4(x - 3y) = -4(2) \implies -4x + 12y = -8 \quad \text{(Equation 3)}
\]

Now you have:
- From Equation 3: \(-4x + 12y = -8\)
- From Equation 2: \(4x + 7y = 27\)

Now you can add these two new equations together to eliminate \( x \).

Thus, the first step in solving the system of equations using elimination is:

**Multiply the first equation by -4.**