Question

Question was provided via image upload.

Explanation:

Problem 7

Step1: Eliminate $x$, scale 2nd eq

Multiply $x + 2y = 16$ by $-3$:
$-3x -6y = -48$

Step2: Add to 1st eq, solve $y$

Add to $3x -9y = 3$:
$$(3x-9y)+(-3x-6y)=3+(-48)$$
$-15y=-45$
$y=3$

Step3: Substitute $y=3$ to find $x$

$x + 2(3)=16$
$x+6=16$
$x=10$

Problem 8

Step1: Eliminate $y$, scale 1st eq

Multiply $2x + 3y =7$ by $2$:
$4x +6y=14$

Step2: Add to 2nd eq, solve $x$

Add to $3x -6y=21$:
$$(4x+6y)+(3x-6y)=14+21$$
$7x=35$
$x=5$

Step3: Substitute $x=5$ to find $y$

$2(5)+3y=7$
$10+3y=7$
$3y=-3$
$y=-1$

Problem 9

Step1: Eliminate $x$, scale 2nd eq

Multiply $3x -5y=20$ by $-3$:
$-9x +15y=-60$

Step2: Add to 1st eq, solve $y$

Add to $9x + y=-4$:
$$(9x+y)+(-9x+15y)=-4+(-60)$$
$16y=-64$
$y=-4$

Step3: Substitute $y=-4$ to find $x$

$9x + (-4)=-4$
$9x=0$
$x=0$

Answer:

1. $\boldsymbol{(10, 3)}$
2. $\boldsymbol{(5, -1)}$
3. $\boldsymbol{(0, -4)}$