Systems of Equations Term Paper

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Systems of Equations

Solve for X and Y

X + Y=6, 2X + Y = 8

7X + 3Y = 14, 5X + 9Y = 10

4X + Y = 16, 2X + 3Y = 24

Y = 25, 8X - 2Y = 14

Using the elimination method for solving simultaneous equations we get

X + Y=6, 2X + Y = 8

X + Y = 6 -- ( [1]

2X + Y = 8 -- ( [2]

( (Changing signs)

Substituting X = 2 in [1] we get

+ y = 6

y = 6 -- 2

y = 4

Therefore x = 2 and y = 4

X and y values thus found can be verified by substituting them in any one of the given equations.


2X + Y = 8

L.H.S = R.H.S

7X + 3Y = 14, 5X + 9Y = 10

7X + 3Y = 14 -- ((1)

5X + 9Y = 10 -- >(2)

Multiplying (1) by 5, we get

35x + 15y = 70 -- ( (3)

Multiplying (2) by 7, we get

35x + 63y = 70 -- ( (4)

(3)- (4),we get

-48y = 0

y = 0

Substituting y = 0 in [1] we get

7x + 0 = 14

=>7x = 14

Therefore x = 2 and y = 0

X and y.....

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