Question

find the solution of the system of equations. 2x + 3y = -4 x + 9y = 13

Explanation:

Step1: Solve the second equation for x

From \( x + 9y = 13 \), we can express \( x \) as \( x = 13 - 9y \).

Step2: Substitute x into the first equation

Substitute \( x = 13 - 9y \) into \( 2x + 3y = -4 \):
\[

$$\begin{align*} 2(13 - 9y) + 3y &= -4\\ 26 - 18y + 3y &= -4\\ 26 - 15y &= -4 \end{align*}$$

\]

Step3: Solve for y

Subtract 26 from both sides:
\[
-15y = -4 - 26\\
-15y = -30
\]
Divide both sides by -15:
\[
y = \frac{-30}{-15} = 2
\]

Step4: Substitute y back to find x

Substitute \( y = 2 \) into \( x = 13 - 9y \):
\[
x = 13 - 9\times2 = 13 - 18 = -5
\]

Answer:

The solution of the system is \( x = -5 \), \( y = 2 \)