Question

Rectangle FGHJ has diagonals FH and JG that intersect at M. If FJ=−3x+5y, FM=3x+y, GH=11, and GM=13, find the values of x and y. Explain your answer.

Answer 1

x=3 y=4

Explanation:

-3x + 5y = 11

+ 3x + y = 13

Add the equation (add the 5y and y. Then add the 11 and 13). The threes cancel each other out. It then leaves us with the equation:

6y = 24

Divide both sides by 6 to isolate the variable.

y=4.

Then just substitute the variable into any of the equations above. (I chose the equation on top)

-3x + 5(4) = 11

Then solve

-3x + 20 = 11 (then subtract 20 from both sides)

-3x = -9 (then divide both sides by -3)

x=3