Question
A variable needs to be eliminated to solve the system of equations below. Choose the correct first step.
6, x, plus, 4, y, equals, minus, 48
6x+4y=
−48
6, x, plus, 7, y, equals, minus, 66
6x+7y=
−66
6, x, plus, 4, y, equals, minus, 48
6x+4y=
−48
6, x, plus, 7, y, equals, minus, 66
6x+7y=
−66
Answers
GPT-4o mini
To eliminate a variable in the given system of equations, we can use the method of elimination. The equations are:
1. \( 6x + 4y = -48 \)
2. \( 6x + 7y = -66 \)
The first step should be to subtract one equation from the other in order to eliminate the \( x \) variable. Since both equations have the same coefficient for \( x \) (which is 6), we can subtract equation 1 from equation 2:
\[
(6x + 7y) - (6x + 4y) = -66 - (-48)
\]
This simplifies to:
\[
3y = -66 + 48
\]
Now you can solve for \( y \).
So, the correct first step is to subtract the first equation from the second one to eliminate \( x \).
1. \( 6x + 4y = -48 \)
2. \( 6x + 7y = -66 \)
The first step should be to subtract one equation from the other in order to eliminate the \( x \) variable. Since both equations have the same coefficient for \( x \) (which is 6), we can subtract equation 1 from equation 2:
\[
(6x + 7y) - (6x + 4y) = -66 - (-48)
\]
This simplifies to:
\[
3y = -66 + 48
\]
Now you can solve for \( y \).
So, the correct first step is to subtract the first equation from the second one to eliminate \( x \).