Question

graph each equation. determine the solution of the system of equations.
$x + 2y = 12$
$7x + 2y = 0$
use the graphing tool to graph the system.

Explanation:

Step1: Eliminate $2y$ via subtraction

Subtract the first equation from the second:
$$(7x + 2y) - (x + 2y) = 0 - 12$$
$$6x = -12$$

Step2: Solve for $x$

Divide both sides by 6:
$$x = \frac{-12}{6} = -2$$

Step3: Substitute $x=-2$ to find $y$

Plug $x=-2$ into $x + 2y = 12$:
$$-2 + 2y = 12$$
$$2y = 12 + 2 = 14$$
$$y = \frac{14}{2} = 7$$

Step4: Verify with the second equation

Check $7x + 2y = 0$:
$$7(-2) + 2(7) = -14 + 14 = 0$$

Answer:

The solution to the system is $x=-2$, $y=7$, or the ordered pair $(-2, 7)$.

To graph:

1. For $x + 2y = 12$:

• x-intercept: when $y=0$, $x=12$ (point $(12, 0)$)
• y-intercept: when $x=0$, $y=6$ (point $(0, 6)$)

1. For $7x + 2y = 0$:

• x-intercept: when $y=0$, $x=0$ (point $(0, 0)$)
• Second point: when $x=-2$, $y=7$ (point $(-2, 7)$)

The two lines intersect at $(-2, 7)$.