Question

solve each system by graphing. check your solution.

1. $y=2x$

$y=2x + 8$

1. $y=\frac{1}{2}x + 7$

$y=\frac{3}{2}x + 3$

1. $y=\frac{1}{3}x + 1$

$y=-3x + 11$

1. $y=x - 4$

$y=x + 1$

1. $y=-x + 3$

$y=x + 1$

1. $4x - y=-1$

$-x + y=x - 5$

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

$y=\frac{1}{2}x + 6$

1. $2x - y=-5$

$-2x - y=-1$

1. $x=-3$

$y=5$

Explanation:

Problem 10

Step1: Identify equations

Equations: $y=2x$ and $y=2x+8$

Step2: Analyze slopes/intercepts

Both have slope $m=2$, $y$-intercepts $(0,0)$ and $(0,8)$. Parallel lines never intersect.

Step1: Identify equations

Equations: $y=\frac{1}{2}x+7$ and $y=\frac{3}{2}x+3$

Step2: Set equal to find $x$

$\frac{1}{2}x+7=\frac{3}{2}x+3$
$7-3=\frac{3}{2}x-\frac{1}{2}x$
$4=x$

Step3: Find $y$ with $x=4$

$y=\frac{1}{2}(4)+7=2+7=9$

Step1: Identify equations

Equations: $y=\frac{1}{3}x+1$ and $y=-3x+11$

Step2: Set equal to find $x$

$\frac{1}{3}x+1=-3x+11$
$\frac{1}{3}x+3x=11-1$
$\frac{10}{3}x=10$
$x=3$

Step3: Find $y$ with $x=3$

$y=\frac{1}{3}(3)+1=1+1=2$

Answer:

No solution

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Problem 11