Answer:
a) (0.333, 13.11)
b) (1, 9)
Explanation:
a)
5x+3y=41
2x+3y=40
[The steps are labelled so they can be referenced in the subsequent problems]
A. Rearrange one of the two equations so as to isolate the x or y to one side. I'll use 2x+3y=40:
2x+3y=40
2x = 40-3y
x = (40-3y)/2
B. Now use that expression of x in the other equation:
5x+3y=41
5((40-3y)/2)+3y=41
(200-15y)/2 +3y = 41
100 - 7.5y + 3y = 41
-4.5y = - 59
y = 13.11
C. Now use y=13.11 in either equation to find x:
2x+3y=40
2x+3*(13.11)=40
2x + 39.33 = 40
2x = 0.67
x = 0.333
D. Answer: The lines intersect at (0.333, 13.11)
b)
x+7y=64
x+3y=28
A.
x+7y=64
x=64-7y
B.
x+3y=28
(64-7y)+3y=28
64-4y = 28
-4y = -36
y = 9
C.
x=64-7y
x=64-7*9
x = 1
D. Answer: The lines intersect at (1, 9)
See the attached graph for proof of the points of intersection.
HELPPP PROVIDED (I hope)