Question

systems of linear equations: tutorial
now graph the equations to confirm the solutions that you just found algebra
$2x + y = 8$
$6x - 2y = -6$

Explanation:

Step1: Rewrite equations to slope-intercept form

For $2x + y = 8$:
$y = -2x + 8$
For $6x - 2y = -6$:
$-2y = -6x -6$
$y = 3x + 3$

Step2: Find intercepts for first line

x-intercept (set $y=0$):
$0 = -2x + 8 \implies x=4$ → Point $(4, 0)$
y-intercept (set $x=0$):
$y = -2(0) + 8 \implies y=8$ → Point $(0, 8)$

Step3: Find intercepts for second line

x-intercept (set $y=0$):
$0 = 3x + 3 \implies x=-1$ → Point $(-1, 0)$
y-intercept (set $x=0$):
$y = 3(0) + 3 \implies y=3$ → Point $(0, 3)$

Step4: Solve for intersection algebraically

Set $-2x + 8 = 3x + 3$
$8 - 3 = 3x + 2x$
$5 = 5x \implies x=1$
Substitute $x=1$ into $y=-2x+8$:
$y = -2(1) + 8 = 6$ → Intersection $(1, 6)$

Answer:

1. For $y=-2x+8$, plot points $(4,0)$ and $(0,8)$, then draw a line through them.
2. For $y=3x+3$, plot points $(-1,0)$ and $(0,3)$, then draw a line through them.
3. The two lines intersect at $(1, 6)$, which is the solution to the system.