Question

which ordered pair satisfies the system of equations below?
$3x - y = 8$
$x + y = 2$
$\bigcirc\\ (3, -1)$
$\bigcirc\\ (2.5, 0.5)$
$\bigcirc\\ (2.5, -0.5)$
$\bigcirc\\ (5, -3)$
3 multiple choice 4 points
if $x + y = -10$ and $x - y = 2$, what is the value of $x$?
$\bigcirc\\ -4$
$\bigcirc\\ 4$
$\bigcirc\\ -6$
$\bigcirc\\ 6$
4 multiple choice 4 points
what is the value of the $y$-coordinate of the solution to the system of equations $x + 2y = 9$ and $x - y = 3$?
$\bigcirc\\ 2$
$\bigcirc\\ 3$
$\bigcirc\\ 6$
$\bigcirc\\ 5$

Explanation:

Step1: Solve first system via elimination

Add the two equations:
$$3x - y + x + y = 8 + 2$$
$$4x = 10$$
$$x = \frac{10}{4} = 2.5$$
Substitute $x=2.5$ into $x+y=2$:
$$2.5 + y = 2$$
$$y = 2 - 2.5 = -0.5$$

Step2: Solve second system via elimination

Add the two equations:
$$x + y + x - y = -10 + 2$$
$$2x = -8$$
$$x = \frac{-8}{2} = -4$$

Step3: Solve third system via substitution

From $x - y = 3$, get $x = y + 3$. Substitute into $x + 2y = 9$:
$$(y + 3) + 2y = 9$$
$$3y + 3 = 9$$
$$3y = 6$$
$$y = \frac{6}{3} = 2$$

Answer:

1. (2.5, -0.5)
2. -4
3. 2