Question

Solve using substitution.

x − 3y = 8
4x − 7y = 17

(
,
)

Answer 1

To solve the system of equations using substitution, we will first solve one of the equations for one variable and then substitute that expression into the other equation.

Given the equations:

1. \( x - 3y = 8 \) (Equation 1)
2. \( 4x - 7y = 17 \) (Equation 2)

### Step 1: Solve Equation 1 for \( x \)

From Equation 1:

\[
x = 3y + 8
\]

### Step 2: Substitute \( x \) in Equation 2

Now we will substitute \( x \) in Equation 2:

\[
4(3y + 8) - 7y = 17
\]

### Step 3: Simplify and solve for \( y \)

Distributing the 4:

\[
12y + 32 - 7y = 17
\]

Combine like terms:

\[
12y - 7y + 32 = 17
\]
\[
5y + 32 = 17
\]

Now, subtract 32 from both sides:

\[
5y = 17 - 32
\]
\[
5y = -15
\]

Divide by 5:

\[
y = -3
\]

### Step 4: Substitute \( y \) back into the expression for \( x \)

Now that we have \( y \), we substitute it back into the expression for \( x \):

\[
x = 3(-3) + 8
\]

Calculate:

\[
x = -9 + 8
\]
\[
x = -1
\]

### Solution

The solution to the system of equations is:

\[
(x, y) = (-1, -3)
\]

So the final answer is:

\[
(-1, -3)
\]