Pair of Linear Equations : Pair of Linear Equations Class X
Slide 2 : Example 1
Seven years ago A was seven times as old as B was then. Three years from now, A will be three times as old as B then. Represent this algebraically and find their present ages.
Slide 3 : Equations
x – 7 = 7(y - 7)
x + 3 = 3(y + 3) Equations Simplified
x - 7y + 42 = 0 …..(1)
x - 3y - 6 = 0 …..(2)
Slide 4 : Solution by Elimination
x - 7y = - 42 …..(1)
x - 3y = 6 …..(2)
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(1) – (2): -4y = -48
y = 48/4 = 12
Substitute in (2): x – 36 = 6
x = 36 + 6 = 42
A’s present age = 42
B’s present age = 12
Slide 5 : Example 2
x - 7y + 42 = 0 …..(1)
x - 3y - 6 = 0 …..(2)
……………………………….
a1 = 1, b1 = -7, c1 = 42
a2 = 1, b2 = -3, c2 = -6
…………………………………
Slide 6 : Example 3
Sania buys 3 bats and 6 balls for
Rs 3900. Later she buys another bat
and 3 more balls of the same kind
for Rs 1300. Represent this situation
algebraically and find the price of
a bat and that of a ball.
Slide 7 : Equations
3x + 6y = 3900………………..(1)
x + 3y = 1300………………..(2)
Slide 8 : Solution by elimination:
3x + 6y = 3900………………(1)
x + 3y = 1300 ………………(2)
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(1)…………………….. 3x + 6y = 3900…………..(3)
(2)x3…………………. 3x + 9y = 3900……………(4)
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(4)-(3)………………… 3y = 0 y = 0
x = 1300
What’s your conclusion?
Try this using the Cross-Multiplication method.
Slide 9 : Example 3
The cost of 2 kg of apples and 1 kg of grapes is Rs 160 and that of 3 kg of apples and 2 kg of grapes is Rs 300. Represent this situation algebraically and find the price per kg of apples and grapes.
Slide 10 : Equations
2x + y = 160………………..(1)
3x + 2y = 300 ………………..(2)
Slide 11 : Solution by elimination:
2x + y = 160………………..(1)
3x + 2y = 300………………..(2)
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(1)x2…………….. 4x + 2y = 320…………..(3)
(2)…………………. 3x + 2y = 300……………(4)
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(3)-(4)………………… x = 20
(1)……………………. y = 120
What’s your conclusion?
Try this using the Cross-Multiplication method.
Slide 12 : General Linear Equation:
ax + by + c = 0
This represents a line. Graphical Solution
Slide 13 :
Slide 14 : Example 4: Cross-Multiplication
5x – 2y + 10 = 0……………………..(1)
3x + 3y - 9 = 0………………………(2)
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a1 = 5, b1 = -2, c1 = 10
a2 = 3, b2 = 3, c2 = -9
Slide 15 : Line 1 Line 2 Line 1 Line 2