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Question
Solve the following simultaneous equation.
x - 2y = -1 ; 2x - y = 7
Solution
x - 2y = -1 ...(I)
2x - y = 7 ...(II)
Multiply (I) with 2,
2x - 4y = -2 ....(III)
Subtracting (III) from (II)
2x - y = 7
2x - 4y = -2
- + +
3y = 9
∴ y = 3
Putting the value of y in (I) we get,
∴ x - 2y = -1
⇒ x - 2 × 3 = -1
⇒ x - 6 = -1
⇒ x = -1 + 6
⇒ x = 5
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The sum of the two-digit number and the number obtained by interchanging the digits is 132. The digit in the ten’s place is 2 more than the digit in the unit’s place. Complete the activity to find the original number.
Activity: Let the digit in the unit’s place be y and the digit in the ten’s place be x.
∴ The number = 10x + y
∴ The number obtained by interchanging the digits = `square`
∴ The sum of the number and the number obtained by interchanging the digits = 132
∴ 10x + y + 10y + x = `square`
∴ x + y = `square` .....(i)
By second condition,
Digit in the ten’s place = digit in the unit’s place + 2
∴ x – y = 2 ......(ii)
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∴ x = `square`, y = `square`
Ans: The original number = `square`
