Question

Solve the given system of equations. 2x + 8y = 5 24x - 4y = -15

Answer 1

SOLUTION

TO DETERMINE

To solve the given system of equations

2x + 8y = 5

24x - 4y = - 15

EVALUATION

Here the system of equations

2x + 8y = 5 - - - - - - - (1)

24x - 4y = - 15 - - - - - (2)

Multiplying equation (2) by 2 we get

48x - 8y = - 30 - - - - - - (3)

Equation (1) + Equation (3) gives

50x = - 25

$\displaystyle \sf{ \implies \: x = - \frac{25}{50} }$

$\displaystyle \sf{ \implies \: x = - \frac{1}{2} }$

From Equation (1) we get

$\displaystyle \sf{ \: 2 \times - \frac{1}{2} + 8y = 5}$

$\displaystyle \sf{ \implies \: - 1 + 8y = 5}$

$\displaystyle \sf{ \implies \: 8y = 6}$

$\displaystyle \sf{ \implies \: y = \frac{6}{8} }$

$\displaystyle \sf{ \implies \: y = \frac{3}{4} }$

Hence the required solution is

$\displaystyle \sf{ x = - \frac{1}{2} \: ,\: y = \frac{3}{4} }$

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