Question

y=2x-9
-x-8y=21
substitution

Answer 1

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

1. \( y = 2x - 9 \) (Equation 1)
2. \( -x - 8y = 21 \) (Equation 2)

### Step 1: Substitute Equation 1 into Equation 2

We'll substitute the expression for \( y \) from Equation 1 into Equation 2:

\[
-x - 8(2x - 9) = 21
\]

### Step 2: Simplify

Now, distribute the -8 in the equation:

\[
-x - 16x + 72 = 21
\]

Combine like terms:

\[
-17x + 72 = 21
\]

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

Subtract 72 from both sides:

\[
-17x = 21 - 72
\]
\[
-17x = -51
\]

Now, divide by -17:

\[
x = \frac{-51}{-17} = 3
\]

### Step 4: Substitute \( x \) back into Equation 1 to find \( y \)

Now that we have \( x = 3 \), substitute it back into Equation 1:

\[
y = 2(3) - 9
\]
\[
y = 6 - 9
\]
\[
y = -3
\]

### Conclusion

The solution to the system of equations is:

\[
x = 3, \quad y = -3
\]

Thus, the point of intersection is \( (3, -3) \).