Question

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

$y = \frac{1}{4}x - 4$

1. $y = -1$

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

Explanation:

For System 3: $y = -\frac{1}{2}x - 1$ and $y = \frac{1}{4}x - 4$

Step1: Set equations equal

$-\frac{1}{2}x - 1 = \frac{1}{4}x - 4$

Step2: Multiply by 4 to eliminate denominators

$-2x - 4 = x - 16$

Step3: Isolate x terms

$-2x - x = -16 + 4$
$-3x = -12$

Step4: Solve for x

$x = \frac{-12}{-3} = 4$

Step5: Substitute x=4 into $y=-\frac{1}{2}x-1$

$y = -\frac{1}{2}(4) - 1 = -2 - 1 = -3$

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For System 4: $y = -1$ and $y = -\frac{5}{2}x + 4$

Step1: Substitute y=-1 into second equation

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

Step2: Isolate x term

$-\frac{5}{2}x = -1 - 4$
$-\frac{5}{2}x = -5$

Step3: Solve for x

$x = (-5) \times (-\frac{2}{5}) = 2$

Answer:

System 3 solution: $(4, -3)$
System 4 solution: $(2, -1)$

*(To graph:
For System3:

• $y=-\frac{1}{2}x-1$: y-intercept $(0,-1)$, slope $-\frac{1}{2}$; plot $(0,-1)$, move 2 right 1 down to $(2,-2)$
• $y=\frac{1}{4}x-4$: y-intercept $(0,-4)$, slope $\frac{1}{4}$; plot $(0,-4)$, move 4 right 1 up to $(4,-3)$

For System4:

• $y=-1$: horizontal line through $(0,-1)$
• $y=-\frac{5}{2}x+4$: y-intercept $(0,4)$, slope $-\frac{5}{2}$; plot $(0,4)$, move 2 right 5 down to $(2,-1)$)*