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Solve the Following Systems of Equations: 23x − 29y = 98 29x − 23y = 110 - Mathematics

Solve the following systems of equations:

23x − 29y = 98
29x − 23y = 110

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Solution

The given system of equation is

23x − 29y = 98 ....(i)

29x − 23y = 110 ...(ii)

Adding equation (i) and equation (ii), we get

23x + 29x - 29y - 23y = 98 + 110

=> 52x - 52y = 208

=> 52 (x - y) = 208

`=> x - y = 208/52 = 4`

=> x - y - 4 ...(iii)

Subtracting equation (i) by equation (ii), we get

29x - 23x - 23y + 29y = 110 - 98

=> 6x + 6y = 12

=> 6(x + y) = 12

`=> x + y = 12/6 = 2`

=> x = y = 2 ...(iv)

Adding equation (iii) and equation (iv), we get

2x = 2 + 4 = 6

Putting x = 3 in equation (iv), we get

3 + y = 2

=>? y = 2- 3 = -1

Hence, solution of the given system of equation is x = 3 , y = -1

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APPEARS IN

RD Sharma Class 10 Maths
Chapter 3 Pair of Linear Equations in Two Variables
Exercise 3.3 | Q 45 | Page 46
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