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1

LINEAR EQUATIONS AND THEIR SOLUTION

1. X-3Y=-6………….1

5X+3Y=42…………2

ANS: By adding the equations, 3y and -3y will cancel out, then

6x = 36

Now dividing by 6 on both sides, we get

X = 6

To find the value of y we put x = 6 in equation 1, then

6 -3y = -6

Adding -6 on both sides, we get

-3y = -12

Dividing by – 3 on both sides, we get

y = 4

Hence (x, y) = (6, 4)

2. 2X-6Y=7 …………3

5X-2Y=10 ………..4

ANS: Multiply equation 3 by 2 and multiply equation 4 by -6, we get

4x - 12y = 14

-30x + 12y = -60

Now adding the above equations, we get

-26x = -46

Now dividing by-26 on both sides, we get

X = 46/26 or

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2

LINEAR EQUATIONS AND THEIR SOLUTION

X = 23/13

Now put the value of x in equation 4x - 12y = 14, we get

4(23/13) - 12y = 14

92/13 - 12y = 14

Now multiply by 13 on both sides, we get

92 - 156y = 182

Adding -92 on both sides, we get

-156y = 182

Dividing by -156 on both sides, we get

Y = -91/78

HENCE (x, y) = (23/13, -91/78)

3. 2X+16Y=9………….5

1/4X+4Y=8…………..6

ANS: Multiplying equation 6 by -4, we get

2x + 16y = 9

-x - 16y = 8

Adding above equations, we get

X = 17

Putting the value of x in equation 5, we get

2(17) + 16y = 9

34 + 16y = 9

Now adding -34 on both sides, we get

16y = -25

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3

LINEAR EQUATIONS AND THEIR SOLUTION

Dividing by 16 on both sides, we get

y = -25/16

HENCE (x, y) = (17, -25/16)

4. X-2Y=7………..7

9X+6Y=15……….8

ANS: Multiplying equation 7 by 3, we get

3x - 6y = 21

9x + 6y = 15

Adding the above equations, we get

12x = 36

Dividing by 12 on both sides, we get

x = 3

Now putting the values in equation 7, we get

3 - 2y = 7

Adding -3 on both sides, we get

-2y = 4

Dividing by -2 on both sides, we get

y = -2

HENCE (x, y) = (3, -2)

5. 7/4X-5/2Y=2………..9

1/4X+7/2Y=8……….10

ANS: Multiply both equations with 4, we get

7x - 10y = 8………..A

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