Question

A variable needs to be eliminated to solve the system of equations below. Choose the correct first step.
minus, 3, x, minus, 7, y, equals, 54
−3x−7y=
54
10, x, minus, 7, y, equals, 93
10x−7y=
93

Answer 1

To solve the system of equations given:

1. \( -3x - 7y = 54 \) (Equation 1)
2. \( 10x - 7y = 93 \) (Equation 2)

The best first step to eliminate one of the variables is to eliminate \( y \) since both equations have the same coefficient for \( y \) but with opposite signs.

You can do this by subtracting Equation 1 from Equation 2:

\[
(10x - 7y) - (-3x - 7y) = 93 - 54
\]

This simplifies as follows:

\[
10x - 7y + 3x + 7y = 93 - 54
\]
\[
(10x + 3x) + (-7y + 7y) = 39
\]
\[
13x = 39
\]

Now you can solve for \( x \).

So, the correct first step is to subtract Equation 1 from Equation 2 to eliminate \( y \).