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 \( 2x + 3y = -4 \):

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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 \( x = -5 \), \( y = 2 \)