Solve the following system of linear equations : 2 x + 5 y =

Q) Solve the following system of linear equations : 2 x + 5 y = – 4 and 4 x – 3 y = 5

Ans: Given equations are:

2 x + 5 y = – 4 …………………… (i)

4 x – 3 y = 5 …………………..(ii)

To get the value of variables, we need to first drop one variable.

Let’s multiply (i) by 3 and (ii) by 5 and add them up:

∴ 3 (2 x + 5 y) + 5 (4 x – 3 y) = 3 (- 4) + 5 x 5

∴ 6 x + 15 y + 20 x – 15 y = – 12 + 25

∴ 26 x = 13

∴ x = $\frac{13}{26} = \frac{1}{2}$

Transferring value of x in equation (i), we get:

2 x + 5 y = – 4

∴ 2 ( $\frac{1}{2}$ ) + 5 y = – 4

∴ 1 + 5 y = – 4

∴ 5 y = – 4 – 1

∴ y = $\frac{- 5}{5}$ = – 1

Therefore, values of x and y are $\frac{1}{2}$ and – 1 respectively.

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