Question

solve the system of equations.$y = -3x + 2LXB0(0, -3)$ $(1, -2)$ $(2, -4)$

Explanation:

Step1: Compare the two equations

Notice that $y = -3x + 2$ and $y = 2 - 3x$ are identical, since addition is commutative ($-3x + 2 = 2 - 3x$). This means they represent the same line, so there are infinitely many solutions.

Step2: Test each ordered pair in the equation

For $(0, 2)$: Substitute $x=0, y=2$ into $y=-3x+2$:
$2 = -3(0) + 2 \implies 2=2$, which is true.

For $(1, -1)$: Substitute $x=1, y=-1$ into $y=-3x+2$:
$-1 = -3(1) + 2 \implies -1=-1$, which is true.

For $(2, -1)$: Substitute $x=2, y=-1$ into $y=-3x+2$:
$-1 = -3(2) + 2 \implies -1=-4$, which is false.

For $(0, -3)$: Substitute $x=0, y=-3$ into $y=-3x+2$:
$-3 = -3(0) + 2 \implies -3=2$, which is false.

For $(1, -2)$: Substitute $x=1, y=-2$ into $y=-3x+2$:
$-2 = -3(1) + 2 \implies -2=-1$, which is false.

For $(2, -4)$: Substitute $x=2, y=-4$ into $y=-3x+2$:
$-4 = -3(2) + 2 \implies -4=-4$, which is true.

Answer:

Number of solutions: infinitely many solutions
Valid ordered pairs:
(0, 2)
(1, -1)
(2, -4)