Question 508369: Solve the equations using elimination & substitution method :
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5x-2y=20
x+3y=-10
Answer by Maths68(1474)   (Show Source):
You can put this solution on YOUR website! By Substitution Method
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5x-2y=20 ...........(1)
x+3y=-10 ...........(2)
Take (2)
x+3y=-10
x=-10-3y
Put the value of x in (1)
5x-2y=20 ...........(1)
5(-10-3y)-2y=20
-50-15y-2y=20
-17y=20+50
-17y=70
Divide above equation by -17
-17y/-17=70/-17
y=-70/17
Put the value of y in (2)
x+3(-70/17)=-10
Multiply above equation by 17
17(x+3(-70/17))=-10 * 17
17x+3(-70)=-170
17x-210=-170
17x=-170+210
17x=40
Divide above equation by 17
17x/17=40/17
x=40/17
(x,y)=(40/17, -70/17)
By Elimination Method
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5x-2y=20 ...........(1)
x+3y=-10 ...........(2)
Multiply (2) by -5 and add to (1)
-5(x+3y)=-10*-5
-5x-15y=50
5x-2y=20 ...........(1)
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-17y=70
Divide above equation by -17
-17y/-17=70/-17
y=-70/17
Again put the value of y in (2)
x+3(-70/17)=-10
Multiply above equation by 17
17(x+3(-70/17))=-10 * 17
17x+3(-70)=-170
17x-210=-170
17x=-170+210
17x=40
Divide above equation by 17
17x/17=40/17
x=40/17
(x,y)=(40/17, -70/17)
Check
Put the value of x and y in (2)
x+3y=-10 ...........(2)
40/17 + 3(-70/17)=-10
40/17 - 210/17=-10
Taking LCM
(40-210)/17=-10
Multiply above equation by 17
17*(40-210)/17=-10*17
40-210=-10*17
-170=-170
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