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Question
Solve the following pair of linear equation by the elimination method and the substitution method:
3x + 4y = 10 and 2x – 2y = 2
Solution
3x + 4y = 10 and 2x – 2y = 2
By elimination method
3x + 4y = 10 ...(1)
2x – 2y = 2 ...(2)
Multiplying equation (ii) by 2, we get
4x – 4y = 4 ...(3)
3x + 4y = 10
Adding equation (1) and (3), we get
7x + 0 = 14
Dividing both side by 7, we get
x = `14/7`
x = 2
Putting in equation (1), we get
3x + 4y = 10
3(2) + 4y = 10
6 + 4y = 10
4y = 10 – 6
4y = 4
y = `4/4`
y = 1
Hence, answer is x = 2, y = 1
By substitution method
3x + 4y = 10
y = `(10-3x)/4`
2x - 2y = 10
x - y = 1
Putting y = `(10 - 3x)/4` in (2) we get
⇒ `x - (10 - 3x)/4 = 1`
⇒ 4x - 10 + 3x = 4
⇒ 7x = 14
⇒ `x = 14/7`
⇒ x = 2
Putting x = 2 in (1), we get
y = `(10 - 3 xx2)/4`
y = `(10 - 6)/4`
y = `4/4`
y = 1
Hence, x = 2 and y = 1
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