Question

1. $x + 3y = 1$

$-3x - 3y = -15$

1. $-3x + 3y = 4$

$-x + y = 3$

1. $6x + 6y = -6$

$5x + y = -13$

1. $-3x - 4y = 2$

$3x + 3y = -3$

1. $-5x - 8y = 17$

$2x - 7y = -17$

Explanation:

Problem 11)

Step1: Add the two equations

$x + 3y + (-3x - 3y) = 1 + (-15)$
$\Rightarrow -2x = -14$

Step2: Solve for $x$

$x = \frac{-14}{-2} = 7$

Step3: Substitute $x=7$ into first equation

$7 + 3y = 1$
$\Rightarrow 3y = 1 - 7 = -6$
$\Rightarrow y = \frac{-6}{3} = -2$

Problem 13)

Step1: Multiply second equation by 3

$3(-x + y) = 3\times3$
$\Rightarrow -3x + 3y = 9$

Step2: Subtract new eq from first eq

$-3x + 3y - (-3x + 3y) = 4 - 9$
$\Rightarrow 0 = -5$ (No solution)

Problem 15)

Step1: Simplify first equation by dividing by 6

$x + y = -1$
$\Rightarrow x = -1 - y$

Step2: Substitute $x$ into second equation

$5(-1 - y) + y = -13$
$\Rightarrow -5 -5y + y = -13$
$\Rightarrow -4y = -13 + 5 = -8$
$\Rightarrow y = \frac{-8}{-4} = 2$

Step3: Solve for $x$

$x = -1 - 2 = -3$

Problem 17)

Step1: Add the two equations

$-3x -4y + 3x + 3y = 2 + (-3)$
$\Rightarrow -y = -1$
$\Rightarrow y = 1$

Step2: Substitute $y=1$ into second equation

$3x + 3(1) = -3$
$\Rightarrow 3x = -3 -3 = -6$
$\Rightarrow x = \frac{-6}{3} = -2$

Problem 19)

Step1: Multiply first equation by 2, second by 5

$2(-5x -8y) = 2\times17 \Rightarrow -10x -16y = 34$
$5(2x -7y) = 5\times(-17) \Rightarrow 10x -35y = -85$

Step2: Add the two new equations

$-10x -16y + 10x -35y = 34 + (-85)$
$\Rightarrow -51y = -51$
$\Rightarrow y = \frac{-51}{-51} = 1$

Step3: Substitute $y=1$ into second equation

$2x -7(1) = -17$
$\Rightarrow 2x = -17 +7 = -10$
$\Rightarrow x = \frac{-10}{2} = -5$

Answer:

1. $x=7$, $y=-2$
2. No solution
3. $x=-3$, $y=2$
4. $x=-2$, $y=1$
5. $x=-5$, $y=1$