Question

Find the solution, given the replacement set.

5x - 2y = 6 {(-2, -8), (0, -3), (1, -1), (2, 4), (4, 7)}
a{(-2, -8), (0, -3), (1, -1)}
b{(1, -1), (2, 4), (4, 7)}
c{(-2, -8), (0, -3), (4, 7)}
d{(-2, -8), (2, 4), (4, 7)} which one is it

Answer 1

Plug the values (x,y) into the equation and check if they satisfy the equation.

$(x,y)=(-2,-8) \\ \Downarrow \\ 5 \times (-2) -2 \times (-8)=6 \\ -10+16=6 \\ 6=6 \\ true \\ \\ (x,y)=(0,-3) \\ \Downarrow \\ 5 \times 0 -2 \times (-3) =6 \\ 0+6=6 \\ 6=6 \\ true$

$(x,y)=(1,-1) \\ \Downarrow \\ 5 \times 1-2 \times (-1)=6 \\ 5+2=6 \\ 7=6 \\ not \ true \\ \\ (x,y)=(2,4) \\ 5 \times 2 - 2 \times 4=6 \\ 10-8=6 \\ 2=6 \\ not \ true$

$(x,y)=(4,7) \\ \Downarrow \\ 5 \times 4 -2 \times 7=6 \\ 20-14=6 \\ 6=6 \\ true$

The ordered pairs that satisfy the equation are (-2,-8), (0,-3), and (4,7). The answer is C.