Question

18 multiple choice 2 points
what is the value of the y - coordinate of the solution to the system of equations
x + 2y = 9 and x - y = 3?
○ 5
○ 2
○ 3
○ 6

19 multiple choice 2 points
which ordered pair is the solution of this system of equations?
3x + 2y = 4
-2x + 2y = 24
○ (-4, 8)
○ (2, -5)
○ (2, -1)
○ (-4, -8)

20 multiple choice 2 points
which ordered pair is the solution set for this system of equations?
x + y = 8
y = x - 3
○ (5.5, 2.5)
○ (2.5, 5.5)
○ (4, 4)
○ (4, 1)

Explanation:

Question 18

Step1: Isolate x from 2nd equation

$x = y + 3$

Step2: Substitute into 1st equation

$(y + 3) + 2y = 9$

Step3: Simplify to solve for y

$3y + 3 = 9 \implies 3y = 6 \implies y = 2$

Question 19

Step1: Subtract the two equations

$$\begin{align*} (3x + 2y) - (-2x + 2y) &= 4 - 24\\ 5x &= -20 \end{align*}$$

Step2: Solve for x

$x = \frac{-20}{5} = -4$

Step3: Substitute x into 1st equation

$3(-4) + 2y = 4 \implies -12 + 2y = 4 \implies 2y = 16 \implies y = -8$

Question 20

Step1: Substitute y into 1st equation

$x + (x - 3) = 8$

Step2: Simplify to solve for x

$2x - 3 = 8 \implies 2x = 11 \implies x = 5.5$

Step3: Solve for y using x

$y = 5.5 - 3 = 2.5$

Answer:

1. B. 2
2. D. (-4,-8)
3. A. (5.5, 2.5)