https://file.aiquickdraw.com/mathbot/file/1728761723968upx5b5zl.jpg

The system of equations given in your image is:

\[
\begin{aligned}
x - 4y &= -29 \\
5x + 2y &= 9
\end{aligned}
\]

We are asked to solve this system using the substitution method.

### Step 1: Solve the first equation for \(x\)
From the first equation:
\[
x - 4y = -29
\]
Solve for \(x\):
\[
x = 4y - 29
\]

### Step 2: Substitute the expression for \(x\) into the second equation
Now substitute \(x = 4y - 29\) into the second equation \(5x + 2y = 9\):
\[
5(4y - 29) + 2y = 9
\]

Expand the equation:
\[
20y - 145 + 2y = 9
\]
Simplify:
\[
22y - 145 = 9
\]

### Step 3: Solve for \(y\)
Add 145 to both sides:
\[
22y = 154
\]
Now divide by 22:
\[
y = \frac{154}{22} = 7
\]

### Step 4: Substitute \(y = 7\) back into the expression for \(x\)
Now substitute \(y = 7\) into the equation \(x = 4y - 29\):
\[
x = 4(7) - 29 = 28 - 29 = -1
\]

### Final Answer:
The solution to the system is:
\[
(x, y) = (-1, 7)
\]

Would you like further details or have any questions about this solution?

Here are 5 related questions:
1. How would you solve this system using the elimination method?
2. What happens if you solve for \(y\) first instead of \(x\)?
3. Can you verify this solution by substituting \(x = -1\) and \(y = 7\) into both original equations?
4. How would you solve the same system graphically?
5. What if one equation had a nonlinear term (e.g., \(x^2\))—how would the approach change?

**Tip:** Always substitute your final solution back into the original equations to verify it satisfies both!

Solve the following system of equations: x - 4y = -29 and 5x + 2y = 9 using the substitution method.

Learn how to solve the system of linear equations x - 4y = -29 and 5x + 2y = 9 using the substitution method. This step-by-step guide covers core concepts in linear algebra, including substitution and solving systems of equations. Suitable for high school students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation