Question

Solve using substitution.
7x - 4y = 6
-9x + 4y = -18
(_,_)

Answer 1

To solve the system of equations using substitution, we start with the given equations:

1. \( 7x - 4y = 6 \) (Equation 1)
2. \( -9x + 4y = -18 \) (Equation 2)

First, we can solve one of the equations for one variable and then substitute that into the other equation. Let's solve Equation 1 for \( y \).

**Step 1: Solve for \( y \) in terms of \( x \):**

From Equation 1:
\[
7x - 4y = 6
\]

Rearranging to express \( y \):
\[
-4y = 6 - 7x
\]
\[
4y = 7x - 6
\]
\[
y = \frac{7x - 6}{4}
\]

**Step 2: Substitute \( y \) into Equation 2:**

Now we substitute \( y \) in Equation 2:
\[
-9x + 4y = -18
\]

Substituting for \( y \) gives:
\[
-9x + 4\left(\frac{7x - 6}{4}\right) = -18
\]

The \(4\) cancels out:
\[
-9x + (7x - 6) = -18
\]

Combine terms:
\[
-9x + 7x - 6 = -18
\]
\[
-2x - 6 = -18
\]

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

Add 6 to both sides:
\[
-2x = -12
\]

Divide by -2:
\[
x = 6
\]

**Step 4: Substitute back to find \( y \):**

Now, substitute \( x = 6 \) back into the expression for \( y \):
\[
y = \frac{7(6) - 6}{4}
\]
\[
y = \frac{42 - 6}{4}
\]
\[
y = \frac{36}{4} = 9
\]

**Final Solution:**

The solution to the system of equations is:
\[
(x, y) = (6, 9)
\]

So, the answer in the requested format is:
\[
(6, 9)
\]