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Question
Solve the following set of simultaneous equation.
2x - 7y = 7; 3x + y = 22
Solution 1
2x − 7y = 7 ...(I)
3x + y = 22 ...(II)
y = 22 − 3x ...(III)
Putting y = 22 − 3x in equation (I)
2x − 7(22 − 3x) = 7
2x − 154 + 21x = 7
23x = 7 + 154
23x = 161
x = `161/23`
x = 7
Putting x = 7 in equation (III)
y = 22 − 3 × 7
y = 22 − 21
y = 1
∴ (x, y) = (7, 1)
Solution 2
2x − 7y = 7 ...(1)
3x + y = 22 ...(2)
On multiplying both sides of equation (2) by 7, we get
21x + 7y = 154 ...(3)
By adding equations (1) and (3),
21x + 7y = 154 ...(3)
2x − 7y = 7 ...(1)
23 x = 161
∴ x = `(161)/23`
∴ x = 7
Substituting x = 7 in equation (2), we get
∴ 3x + y = 22
∴ 3(7) + y = 22
∴ 21 + y = 22
∴ y = 22 − 21
∴ y = 1
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