Question

Please help!!

y= 1/2 x + 2
One equation in a system of two linear equations is
shown above. If the system has one solution (x, y),
where x = 2, which of the following could be the
other equation in the system?
A) y = -2x + 4
B) y = -x+ 5
C) y = 2x
D) y = 2x + 1

Answer 1

Answer: B) y = -x+ 5

Explanation:

If the x-value in the solution (x, y) is 2, then the y-value is:

`y=(1)/(2) (2)+2 = (2)/(2) +2=1+2=3`

So the solution coordinate is (2, 3).

Test each of the answer choices to see if whether the y-value is 3 when the x-value is 2. If it's true, then it could be the other equation in the system.

A) y = -2x + 4

`y = -2x + 4\\\y = -2(2) + 4 = -4 + 4 = 0`

B) y = -x+ 5

`y = -x+ 5\\y = -(2) + 5 = 5 - 2 =3`

C) y = 2x

`y=2x\\y=2(2)=4`

D) y = 2x + 1

`y = 2x + 1\\y=2(2)+1=4+1=5`