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

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