olve the systems of equations by using the substitution method. (If the system is dependent, enter a general solution in terms of c. If there is no solution, enter NO SOLUTION.)

5x	 − 	4y	 = 	−13		
y	 = 	5x	 − 	8
(x, y) = 

 



To solve this system of equations using the substitution method, let's proceed with the given equations:

1. \( 5x - 4y = -13 \)
2. \( y = 5x - 8 \)

### Step 1: Substitute the Expression for \( y \) from Equation 2 into Equation 1

Since we already have \( y = 5x - 8 \), substitute this into Equation 1:

\[
5x - 4(5x - 8) = -13
\]

### Step 2: Simplify the Equation

Distribute \( -4 \) in the equation:

\[
5x - 20x + 32 = -13
\]

Combine like terms:

\[
-15x + 32 = -13
\]

### Step 3: Solve for \( x \)

Subtract 32 from both sides:

\[
-15x = -45
\]

Now, divide by \(-15\):

\[
x = 3
\]

### Step 4: Substitute \( x = 3 \) into Equation 2 to Find \( y \)

Now that we have \( x = 3 \), substitute it back into Equation 2:

\[
y = 5(3) - 8
\]

\[
y = 15 - 8
\]

\[
y = 7
\]

### Solution

The solution to the system is:

\[
(x, y) = (3, 7)
\]

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

Here are five related questions you might find helpful:
1. How can you verify the solution to a system of equations?
2. What are the other methods for solving systems of linear equations, besides substitution?
3. How do you identify if a system of equations has no solution?
4. When is a system considered "dependent" in terms of solutions?
5. Can substitution be used efficiently for larger systems, like three equations?

**Tip:** Always check your solution by plugging the values back into the original equations to confirm accuracy.

Solve the systems of equations by using the substitution method: 5x − 4y = −13 and y = 5x − 8.

Explore how to solve the system of equations 5x - 4y = -13 and y = 5x - 8 using the substitution method. This detailed solution provides insights into key algebraic concepts and techniques, suitable for students in Grades 7-9.

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