The Sum of Four Times the First Number and Three Times the Second Number is 15. the Difference of Three Times the First Number and Twice the Second Number is 7. Find the Numbers. - Mathematics

Question

The sum of four times the first number and three times the second number is 15. The difference of three times the first number and twice the second number is 7. Find the numbers.

Sum

Solution

Let the two numbers be x and y respectively.
Then, we have
4x + 3y = 15 ....(i)
3x - 2y = 7 ....(ii)
Multiplying eqn. (i) by 2 and eqn. (ii) by 3, we get
8x + 6y = 30 ....(iii)
9x - 6y = 21 ....(iv)
Adding eqns. (iii) and (iv), we get
17x = 51
⇒ x = 3
⇒ 4(3) + 3y = 15
⇒ 12 + 3y = 15
⇒ 3y = 3
⇒ y = 1
Thus, the two numbers are 3 and 1 respectively.

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Methods of Solving Simultaneous Linear Equations by Elimination Method

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Chapter 8: Simultaneous Linear Equations - Exercise 8.3

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Frank Mathematics [English] Class 9 ICSE

Chapter 8 Simultaneous Linear Equations
Exercise 8.3 | Q 4

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