Question

1.) $-6x + 3y = -9$
$+6x$ $+6x$
$3y = 6x - 9$
$y = \frac{6x}{3} - \frac{9}{3}$
$y = 2x - 3$
$\boxed{y = 2x - 3}$
2.) $5x - y = 1$
3.) $2y - 3x = 10$
4.) $2y + x = 14$
5.) $x - 4y - 8 = 0$
6.) $3y + 18 = -8x + 3$
$-18$ $-18$
$3y = -8x - 15$
$\frac{3y}{3} = \frac{-8x}{3} - \frac{15}{3}$
$\boxed{y = -\frac{8}{3}x - 5}$
7.) $9x - 2y = 7$
8.) $x + 5y = 8x - 20$
9.) $-2(3y - 1) - x = 0$
$-6y + 2 - x = 0$
$-6y = x - 2$
$\frac{-6y}{-6} = \frac{x}{-6} - \frac{2}{-6}$
$\boxed{y = -\frac{1}{6}x + \frac{1}{3}}$
10.) $2x - y = -1$
11.) $3y + 2x + 12 = 0$
12.) $4y + 20 = 5x$
13.) $3(x - 1) = 2x - y$
$3x - 3 = 2x - y$
$-2x + 3$ $-2x + 3$
$x - 3 = -y$
$-1(x - 3) = -1(-y)$
$-x + 3 = y$
$\boxed{y = -x + 3}$
14.) $7x - 1 = 3y + 8$
15.) $9x + 18y = 0$

Explanation:

Let's solve equation 2: \(5x - y = 1\) for \(y\) in terms of \(x\).

Step 1: Isolate the term with \(y\)

We start with the equation \(5x - y = 1\). To isolate \(y\), we can add \(y\) to both sides and subtract 1 from both sides, or we can rearrange the equation. Let's subtract \(5x\) from both sides:
\(-y = 1 - 5x\)

Step 2: Solve for \(y\)

Multiply both sides by \(-1\) to solve for \(y\):
\(y = 5x - 1\)

Answer:

\(y = 5x - 1\)