Question

1. list 2 points that are a solution to the equation 2x + 5y = 10. 2. determine if the point (3, -4) is a solution to the system of linear equations y = -2x + 2 -3x + 2y = -17 solution: 1. 2x + 5y = 10. 2. y = -2x + 2 -3x + 2y = -17. (3, -4)

Explanation:

Step1: Find first point for $2x+5y=10$

Set $x=0$, solve for $y$:
$$2(0) + 5y = 10 \implies 5y=10 \implies y=2$$
Point: $(0, 2)$

Step2: Find second point for $2x+5y=10$

Set $y=0$, solve for $x$:
$$2x + 5(0) = 10 \implies 2x=10 \implies x=5$$
Point: $(5, 0)$

Step3: Test $(3,-4)$ in $y=-2x+2$

Substitute $x=3, y=-4$:
$$-4 = -2(3) + 2 \implies -4 = -6 + 2 \implies -4=-4$$
This is true.

Step4: Test $(3,-4)$ in $-3x+2y=-17$

Substitute $x=3, y=-4$:
$$-3(3) + 2(-4) = -9 -8 = -17$$
This is true.

Answer:

1. Two solution points: $(0, 2)$ and $(5, 0)$
2. The point $(3, -4)$ is a solution to the system of linear equations.