Question

1. solve the system $3x + 4y = -8$ and $x - 2y = 4$. enter your answer as an ordered pair.

Explanation:

Step1: Solve the second equation for x

From \( x - 2y = 4 \), we can express \( x \) in terms of \( y \) by adding \( 2y \) to both sides. So, \( x = 2y + 4 \).

Step2: Substitute x into the first equation

Substitute \( x = 2y + 4 \) into \( 3x + 4y = -8 \). We get \( 3(2y + 4) + 4y = -8 \).
First, distribute the 3: \( 6y + 12 + 4y = -8 \).
Then, combine like terms: \( 10y + 12 = -8 \).
Subtract 12 from both sides: \( 10y = -8 - 12 = -20 \).
Divide both sides by 10: \( y = \frac{-20}{10} = -2 \).

Step3: Find x using the value of y

Now that we know \( y = -2 \), substitute it back into \( x = 2y + 4 \). So, \( x = 2(-2) + 4 = -4 + 4 = 0 \).

Answer:

\((0, -2)\)