Question

Use substitution to solve the linear system of equations. {x = 4 -y = 1/2 x (2, -4), (4,2), (-2,4), (4,-2)

Answer 1

I’m not sure I read the system correctly from what you typed. It can be interpreted a couple of ways. I’ll show the two most plausible readings and their solutions — tell me which one you meant (or re-type the system) and I’ll finish.

1) If the system is
x = 4 − y
y = (1/2)x
(substitute y = (1/2)x into x = 4 − y)
x = 4 − (1/2)x
(3/2)x = 4 → x = 8/3
y = (1/2)(8/3) = 4/3
Solution: (8/3, 4/3). None of the given choices match.

2) If the system is the chain x = 4 − y = (1/2)x (meaning x = 4 − y and 4 − y = (1/2)x), then
x = 4 − y and 4 − y = (1/2)x.
Substitute x = 4 − y into the second:
4 − y = (1/2)(4 − y) → multiply by 2: 8 − 2y = 4 − y → 4 − y = 0 → y = 4, x = 0.
Solution: (0, 4). Not among your choices either.

I checked the four given points (2, −4), (4, 2), (−2, 4), (4, −2) against both interpretations — none satisfy both equations in either case.

Please retype the two equations (for example “x + y = 4” or “x = 4 − y”, and “y = (1/2)x”) and I’ll solve and pick the correct choice.