Question

use substitution to solve the system. 3x + 4y = 11 x - 3y = -18 x = y =

Explanation:

Step1: Solve the second equation for x

From \( x - 3y = -18 \), we can express \( x \) in terms of \( y \) by adding \( 3y \) to both sides. So we get \( x = 3y - 18 \).

Step2: Substitute x into the first equation

Substitute \( x = 3y - 18 \) into the first equation \( 3x + 4y = 11 \). We have:
\( 3(3y - 18)+4y = 11 \)
First, distribute the 3: \( 9y - 54 + 4y = 11 \)
Then, combine like terms: \( 13y - 54 = 11 \)
Add 54 to both sides: \( 13y = 11 + 54 \)
\( 13y = 65 \)
Divide both sides by 13: \( y=\frac{65}{13}=5 \)

Step3: Substitute y back to find x

Now that we know \( y = 5 \), substitute it into the expression we found for \( x \) in Step 1: \( x = 3y - 18 \)
\( x = 3\times5 - 18 \)
\( x = 15 - 18=-3 \)

Answer:

\( x = -3 \), \( y = 5 \)