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Question
Solve the following set of simultaneous equation.
2y - x = 0; 10x + 15y = 105
Solution 1
2y − x = 0
2y = x
∴ x = 2y ...(I)
10x + 15y = 105 ...(II)
Putting x = 2y in equation (II)
10 × 2y + 15y = 105
20y + 15y = 105
35y = 105
y = `105/35`
∴ y = 3
Putting y = 3 in equation (I)
x = 2 × 3 = 6
∴ (x, y) = (6, 3)
Solution 2
2y − x = 0
∴ − x + 2y = 0
∴ x − 2y = 0 ...(1) ...[Multiplying both sides by −1]
10x + 15y = 105
∴ 2x + 3y = 21 ...(2) ...[division by 5 on both sides]
On multiplying both sides of equation (1) by 2, we get
2x − 4y = 0 ...(3)
By subtracting equation (3) from equation (2), we get
2x + 3y = 21 ...(2)
2x − 4y = 0 ...(3)
− +
7y = 21
∴ y = `21/7`
∴ y = 3
Substituting y = 3 in equation (1), we get
∴ x − 2y = 0
∴ x − 2(3) = 0
∴ x − 6 = 0
∴ x = 6
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