SOLUTION: Solve by elinimation 1/3x+2/1=2/1 2/3x-3/5y=1/5 Solve by elinimation x-y=-13 9x-4y=-97 Solve by substitution x+y=7 y=x-1

Algebra ->  Rational-functions -> SOLUTION: Solve by elinimation 1/3x+2/1=2/1 2/3x-3/5y=1/5 Solve by elinimation x-y=-13 9x-4y=-97 Solve by substitution x+y=7 y=x-1      Log On


   



Question 114737: Solve by elinimation
1/3x+2/1=2/1
2/3x-3/5y=1/5
Solve by elinimation
x-y=-13
9x-4y=-97
Solve by substitution
x+y=7
y=x-1

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
1.
Solve by elimination:
%281%2F3%29x%2B2%2F1=2%2F1………………...(1)……multiply both sides by 3
%282%2F3%29x-%283%2F5%29y=1%2F5………………...(2) ……multiply both sides by 3

%281%2F3%293x+%2B+3%2A2%2F1+=+3%2A2%2F1………………...(1)
%282%2F3%293x+-+%283%2F5%293y+=+3%2A1%2F5………………...(2)

x+%2B+6=++6………………...(1) ……..… multiply both sides by 2
2x+-+%289%2F5%29y+=+3%2F5………………...(2)

2x+%2B+12+=++12………………...(1)… subtract (2) from (1)
2x+-+%289%2F5%29y+=+3%2F5………………...(2)

2x+%2B+12+=++12………………...(1)
-2x+-+%289%2F5%29y+=+3%2F5………………...(2)
---------------------------------
2x-2x%2B12-%28-%289%2F5%29y%29+=+12+%96+3%2F5

12+%2B%289%2F5%29y+=+12+%963%2F5….move 12 from the left to the right

%289%2F5%29y+=+12+-%2812%2B3%2F5%29

%289%2F5%29y+=+-%283%2F5%29.......divide -3%2F5 by 9%2F5

y+=+-%283%2F5%29%2F%289%2F5%29.......simplify

y+=+-%283%2A5%29%2F%289%2A5%29.......

y+=+-1%2F3.......

2.
Solve by elimination:
x-y=-13………………...(1) ……..… multiply both sides by 9
9x-4y=-97………………...(2)
9x+-+9y+=+-117………………...(1) …. subtract (2) from (1)
-9x-4y=-97………………...(2)
------------------------------------------
9x+%96+9x+%2B+y+%96+%28-4y%29+=+-+117+%96+%28-97%29
+y+%2B+4y+=+-+117+%2B+97
+5y+=+-20
+5y+=+-20 …………….divide both sides by 5
+%285%2F5%29y+=+-%2820%2F5%29

+y+=+-+4

3.
Solve by substitution:
x%2By=7………………...(1)……… substitute (2) in (1)
y=x-1…………………(2)
x+%2B+%28x-1%29+=+7………………...(1)………
x+%2B+x-1+=+7………………...(1)………
2x+-1+=+7………………...(1)……… move -1 from the left to the right
2x+=+7+%2B+1………………...(1)………
2x+=+8………………...(1)……… divide both sides by 2
%282%2F2%29x+=+8%2F2………………...(1)………
x+=++4………………...(1)……… now substitute x+=++4 in (2)

y=+x-1…………………(2)
y=+4-1…………………(2)
y=+3…………………(2)
So, your solution is:
x+=++4 and y=+3