Question

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

Explanation:

Step1: Solve first system for x

Add the two equations:
$$(x + y) + (x - y) = -10 + 2$$
$$2x = -8$$

Step2: Isolate x for first system

$$x = \frac{-8}{2} = -4$$

Step3: Solve second system for x

Add the two equations:
$$(3x - y) + (x + y) = 8 + 2$$
$$4x = 10$$

Step4: Isolate x for second system

$$x = \frac{10}{4} = 2.5$$

Step5: Find y for second system

Substitute $x=2.5$ into $x+y=2$:
$$2.5 + y = 2 \implies y = 2 - 2.5 = -0.5$$

Step6: Solve third system for y

Substitute $x=-y$ into $x+2y=6$:
$$-y + 2y = 6$$
$$y = 6$$

Step7: Find x for third system

$$x = -y = -6$$

Answer:

1. -4
2. (2.5, -0.5)
3. (-6, 6)