use substitution to solve the system
2x-5y=-8
3x-1=y

To solve the system of equations using the substitution method:

\[
2x - 5y = -8 \quad \text{(Equation 1)}
\]
\[
3x - 1 = y \quad \text{(Equation 2)}
\]

### Step 1: Solve one equation for one variable
Equation 2 is already solved for \( y \):

\[
y = 3x - 1
\]

### Step 2: Substitute the expression for \( y \) into Equation 1
Substitute \( y = 3x - 1 \) into Equation 1:

\[
2x - 5(3x - 1) = -8
\]

### Step 3: Simplify and solve for \( x \)
Distribute the \(-5\) across the terms in the parentheses:

\[
2x - 15x + 5 = -8
\]

Combine like terms:

\[
-13x + 5 = -8
\]

Subtract 5 from both sides:

\[
-13x = -13
\]

Finally, divide by \(-13\):

\[
x = 1
\]

### Step 4: Substitute the value of \( x \) back into Equation 2 to solve for \( y \)
Substitute \( x = 1 \) into \( y = 3x - 1 \):

\[
y = 3(1) - 1 = 3 - 1 = 2
\]

### Solution
The solution to the system of equations is:

\[
x = 1, \quad y = 2
\]

Would you like more details or have any questions? Here are some related problems you might find interesting:

1. Solve the system using substitution: \(2x + y = 7\) and \(y = x + 3\).
2. Use substitution to solve \(4x - y = 2\) and \(y = 2x - 5\).
3. Solve the system \(x + 2y = 5\) and \(3x - y = 4\) using substitution.
4. Determine the solution for \(x = 2y + 1\) and \(y = x - 3\) by substitution.
5. Solve the equations \(5x + 3y = 1\) and \(y = 4x - 2\) using substitution.

**Tip:** When using substitution, it's often easiest to start with the equation that is already solved for one variable. This simplifies the substitution process.

Learn how to solve a system of equations using the substitution method with a detailed step-by-step solution. This problem covers linear equations and the substitution method. Suitable for students in Grades 7-9.

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