Question

Solve the following pair of linear equations

4x -2y =9

3x+4y =4​

Answer 1

4x -2y =9 -----(i)

3x +4y =4 ----(ii)

equation (i) is multiplied with 2

equation (ii) is multiplied with 1

Then it becomes

8x- 4y=18

3x+ 4y =4

after subtracting between equation (i) and (ii) we get

11x =22

therefore x= 22÷11

= 2

Now puting the value of x in equation (i)

4x- 2y =9

4(2)- 2y=9

or, 8- 2y= 9

or, -2y =9– 8

or, -2y = 1

or, y= 1÷2

y = 0.5

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Answer 2

Answer

$\sf \dashrightarrow 4x - 2y = 9 \: \: --- (i)$

$\sf \dashrightarrow 3x + 4y = 4 \: \: --- (ii)$

By first equation,

$\sf \dashrightarrow 4x - 2y = 9$

$\sf \dashrightarrow 4x = 9 + 2y$

$\sf \dashrightarrow x = \dfrac{9 + 2y}{4}$

Now, we can find the value of y by second equation.

$\sf \dashrightarrow 3x + 4y = 4$

$\sf \dashrightarrow 3 \bigg( \dfrac{9 + 2y}{4} \bigg) + 4y = 4$

$\sf \dashrightarrow \dfrac{27 + 6y}{4} + 4y = 4$

$\sf \dashrightarrow \dfrac{27 + 6y + 16y}{4} = 4$

$\sf \dashrightarrow \dfrac{27 + 22y}{4} = 4$

$\sf \dashrightarrow 27 + 22y = 4 \times 4$

$\sf \dashrightarrow 27 + 22y = 16$

$\sf \dashrightarrow 22y = 16 - 27$

$\sf \dashrightarrow 22y = -11$

$\sf \dashrightarrow y = \dfrac{-11}{22}$

$\sf \dashrightarrow y = \dfrac{-1}{2}$

Now, we can find the value of x by first equation.

$\sf \dashrightarrow 4x - 2y = 9$

$\sf \dashrightarrow 4x - 2 \bigg( \dfrac{-1}{2} \bigg) = 9$

$\sf \dashrightarrow 4x - \dfrac{-2}{2} = 9$

$\sf \dashrightarrow 4x - (-1) = 9$

$\sf \dashrightarrow 4x + 1 = 9$

$\sf \dashrightarrow 4x = 9 - 1$

$\sf \dashrightarrow 4x = 8$

$\sf \dashrightarrow x = \dfrac{8}{4}$

$\sf \dashrightarrow x = 2$

Hence, the values of x and y are $\bf \dfrac{-1}{2}$ and 2 respectively.