Question

name myles
solve systems of equations by graphing practice
solve each system of equations by graphing. check the solution. (examples 1–4)

1. $y = x + 4$ $y = -2x - 2$
2. $y - \frac{1}{2}x = -1$ $y = \frac{1}{2}x + 4$
3. $y + \frac{1}{4}x = 1$ $y = \frac{1}{4}x + 1$
4. $x = -3$ $y = 5$

Explanation:

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Problem 1

Step1: Find intersection algebraically

Set $x+4=-2x-2$
$x+2x=-2-4$
$3x=-6$
$x=-2$
Substitute $x=-2$ into $y=x+4$: $y=-2+4=2$

Step2: Verify the solution

Check $y=-2x-2$: $y=-2(-2)-2=4-2=2$, which matches.

Answer:

(Problem 1):
The solution is $(-2, 2)$

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Problem 2

Step1: Rewrite first equation

$y-\frac{1}{2}x=-1$ becomes $y=\frac{1}{2}x-1$

Step2: Analyze line slopes

Both lines have slope $\frac{1}{2}$, so they are parallel (no intersection).