Question

solving systems of equations by graphing
solve each system by graphing.

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

$y=-\frac{7}{3}x+4$
one solution

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

$y=2x-2$
one solution

1. $y=-\frac{1}{7}x-3$

$y=4$

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

$y=-\frac{8}{3}x+4$

Explanation:

Step1: Solve system 1 algebraically

Set $\frac{1}{3}x - 4 = -\frac{7}{3}x + 4$
Multiply by 3: $x - 12 = -7x + 12$
$x + 7x = 12 + 12$
$8x = 24$
$x = 3$
Substitute $x=3$: $y=\frac{1}{3}(3)-4=1-4=-3$

Step2: Solve system 2 algebraically

Set $\frac{1}{3}x + 3 = 2x - 2$
Multiply by 3: $x + 9 = 6x - 6$
$9 + 6 = 6x - x$
$15 = 5x$
$x = 3$
Substitute $x=3$: $y=2(3)-2=6-2=4$

Step3: Solve system 3 algebraically

Set $-\frac{1}{7}x - 3 = 4$
$-\frac{1}{7}x = 7$
$x = -49$
$y=4$

Step4: Solve system 4 algebraically

Set $-\frac{2}{3}x - 2 = -\frac{8}{3}x + 4$
Multiply by 3: $-2x - 6 = -8x + 12$
$-2x + 8x = 12 + 6$
$6x = 18$
$x = 3$
Substitute $x=3$: $y=-\frac{2}{3}(3)-2=-2-2=-4$

Answer:

1. Solution: $(3, -3)$
2. Solution: $(3, 4)$
3. Solution: $(-49, 4)$
4. Solution: $(3, -4)$