Let's solve the system of equations:

\[
\begin{aligned}
-5x + 4y &= -5 \quad \text{(Equation 1)} \\
x &= 5y + 22 \quad \text{(Equation 2)}
\end{aligned}
\]

### Step 1: Substitute Equation 2 into Equation 1
Substitute \(x = 5y + 22\) into the first equation:

\[
-5(5y + 22) + 4y = -5
\]

### Step 2: Distribute and simplify
Distribute \(-5\) through the terms inside the parentheses:

\[
-25y - 110 + 4y = -5
\]

Combine like terms:

\[
-21y - 110 = -5
\]

### Step 3: Solve for \(y\)
Add 110 to both sides of the equation:

\[
-21y = 105
\]

Divide by \(-21\):

\[
y = \frac{105}{-21} = -5
\]

### Step 4: Solve for \(x\)
Substitute \(y = -5\) back into Equation 2:

\[
x = 5(-5) + 22 = -25 + 22 = -3
\]

### Solution
The solution to the system of equations is:
\[
\boxed{x = -3, \, y = -5}
\]

Would you like any details or further explanations?

Here are 5 related questions:
1. How would you solve a system of equations using the elimination method?
2. What is the graphical interpretation of this solution?
3. How do you solve systems of equations with three variables?
4. Can systems of linear equations have no solution or infinite solutions?
5. How do substitution and elimination methods compare in solving systems of equations?

**Tip:** Always double-check your solution by substituting the values back into the original equations.

Discover how to solve a system of linear equations using substitution with the problem -5x + 4y = -5 and x = 5y + 22. This detailed guide covers essential algebraic techniques, suitable 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