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LINEAR EQUATIONS AND THEIR SOLUTIONS

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Mathematics

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Study Guide

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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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Just what I was looking for! Super helpful.

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