Use the substitition to solve the system (y=2-x/2 and below this equation is this one x^2+4y=8?

Question

possible anwsers are the following:
a. (-2,3), (2,1)
b. (-2,3), (4,0)
c. (0,2), (4,0)
d. (0,2), (2,1)

Answer 1

d)

Plug it in:

x^2 + 4(2 - (1/2)x) = 8
x^2 + 8 - 2x = 8
x^2 - 2x = 0
x(x-2) = 0
x = 0 or x = 2

Plug back in:

y = 2 - 0/2 ==> y = 2
(0,2)

y = 2 - 2/2 ==> y = 1
(2,1)

Answer 2

Hi,

Answer D is correct.

If y = 2 - x/2 is graphed you have a parabola opening down from a vertex at (0,2). If you graph y = 2 - x/2 or y = -½x + 2, this gives a straight line through a y intercept of (0,2) and (2,1).

The 2 graphs intersect at both the y intercept of (0,2) and at the point (2,1).

To verify this, substitute both points in the 2 equations:

For (0,2), substitute x = 0
y = 2 - x/2 = 2 - 0/2 = 2 - 0 = 2, so y solves to 2.

y = -½x + 2 = -½(0) + 2 = 0 + 2 = 2 , so y solves to 2.

For (2,1), substitute x = 2
y = 2 - x/2 = 2 - 2/2 = 2 - 1 = 1, so y solves to 1.

y = -½x + 2 = -½(2) + 2 = -1 + 2 = 1 , so y solves to 1.


I hope that helps!! :-)

Answer 3

They ask for substitution, so the logical choice would be to use the first equation as a value of y. Substitute into the second equation to get x^2 + 4(2-(x/2)) = 8.

x^2 + 8 - 2x = 8
x^2 - 2x = 0
x(x-2) = 0
x = 0, x = 2

The only possible answers must have x = 0 and x = 2, so that would be D.

Answer 4

x² + 4.(2 - x) / 2 = 8
x² + 4 - 2x = 8
x² - 2x = 4
x.(x - 2) = 0
x = 0 , x = 2
y = 2 , y = 1
Solution is (0,2) , (2,1)
ANSWER d.