https://file.aiquickdraw.com/mathbot/file/1726700691058u665ebqo.jpg

To solve the system of equations:

\[
\begin{aligned}
-3x + 7y &= -94 \\
-3x + 4y &= -64
\end{aligned}
\]

The goal is to eliminate one of the variables, and the first step should focus on that.

### Step 1: Eliminate \( x \)
Since the coefficient of \( x \) in both equations is the same (-3), subtract the second equation from the first to eliminate \( x \).

\[
(-3x + 7y) - (-3x + 4y) = -94 - (-64)
\]

This simplifies to:

\[
(7y - 4y) = -94 + 64
\]
\[
3y = -30
\]
\[
y = -10
\]

Now that \( y \) is found, the next step would be to substitute \( y = -10 \) back into one of the original equations to solve for \( x \).

Would you like further details on solving for \( x \) or have any questions about the elimination method?

### Related Questions:
1. What are other methods to solve systems of equations besides elimination?
2. How can substitution be applied to this system instead of elimination?
3. What happens when both variables have different coefficients in both equations?
4. How can you verify the solution of a system of equations?
5. Can a system of linear equations have no solution or infinitely many solutions?

**Tip**: Always check for the best first step by analyzing the coefficients of the variables; sometimes, multiplying one or both equations first helps.

A variable needs to be eliminated to solve the system of equations below. Choose the correct first step.
-3x + 7y = -94
-3x + 4y = -64

Learn how to solve a system of equations using the elimination method for the problem -3x + 7y = -94 and -3x + 4y = -64. The step-by-step solution focuses on eliminating the variable x by subtracting the equations. This method is useful for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation