Question

1. $4x + y = -10$

$8x + 3y = -22$

1. $-4x + 9y = 29$

$2x - 7y = -27$

Explanation:

Problem 6:

Step1: Solve for y from first equation

From \(4x + y = -10\), we get \(y = -10 - 4x\).

Step2: Substitute y into second equation

Substitute \(y = -10 - 4x\) into \(8x + 3y = -22\):
\[

$$\begin{align*} 8x + 3(-10 - 4x) &= -22\\ 8x - 30 - 12x &= -22\\ -4x - 30 &= -22\\ -4x &= 8\\ x &= -2 \end{align*}$$

\]

Step3: Find y using x = -2

Substitute \(x = -2\) into \(y = -10 - 4x\):
\[
y = -10 - 4(-2) = -10 + 8 = -2
\]

Step1: Multiply second equation by 2

Multiply \(2x - 7y = -27\) by 2: \(4x - 14y = -54\)

Step2: Add to first equation

Add \(-4x + 9y = 29\) and \(4x - 14y = -54\):
\[

$$\begin{align*} (-4x + 9y) + (4x - 14y) &= 29 + (-54)\\ -5y &= -25\\ y &= 5 \end{align*}$$

\]

Step3: Find x using y = 5

Substitute \(y = 5\) into \(2x - 7y = -27\):
\[

$$\begin{align*} 2x - 7(5) &= -27\\ 2x - 35 &= -27\\ 2x &= 8\\ x &= 4 \end{align*}$$

\]

Answer:

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

Problem 8: