Question

A pair of equations is shown below.
x + y = 2
y = 1/2x + 5

If the two equations are graphed, at what point do the lines representing the two equations intersect?

(4, −2)
(−2, 4)
(2, 5)
(5, −2)

My guess would be A..

Answer 1

Suggestion: Use parentheses so that there's no doubt regarding what you mean by
y = 1/2x + 5 . If your 1/2 is the slope, then it's essential that you enclose that 1/2 in parentheses. Otherwise your y = 1/2x + 5 could be interpreted as

y = 1/(2x) + 5, which is an entirely different function.

Answer 2

Have you tried graphing your version of this function? If you do this accurately, it should be straightforward to determine the point of intersection.

Answer 3

at the intersection (x,y) is the same for both equations
write the expression for x or y from equation 1 and set it equal to the same expression in equation 2
solve for the one unknown in that equation
use that value in the expression to calculate the value for the other variable

Answer 4

I have tried graphing it @mathmale, but it ends terribly wrong since I am very confused as to what to graph.