Question

8. What is the solution to the system? y = 1/2x, 2x + 3y = 28

A) (2, 3)
B) (8, 4)
C) (7, 3.5)
D) (2, 14)

Answer 1

`y=(1)/(2)x \\ 2x+3y=28 \\ \\ \hbox{substitute } (1)/(2)x \hbox{ for y in the second equation:} \\ 2x+3 ((1)/(2)x)=28 \\ 2x+(3)/(2)x=28 \ \ \ \ \ |* 2 \\ 4x+3x=56 \\ 7x=56 \ \ \ \ \ \ \ \ \ \ \ \ |/ 7 \\ x=8 \\ \\ y=(1)/(2)x=(1)/(2) * 8=4 \\ \\ \boxed{(x,y)=(8,4)} \Leftarrow \hbox{answer B}`