Question

3/2x-y=1/4;x+1/2y=1
solve by substitution​

Answer 1

according to me I think it is correct

Answer 2

$x = \frac{9}{14} \: and \: y = \frac{5}{7}$

Given:- Equation 1= $\frac{3}{2} x - y = \frac{1}{4}$

Equation 2 = $x + \frac{1}{2} y = 1$

To Find:- Solve for x and y

Solution :-

Using Equation 2 to find a substitute

$x + \frac{1}{2} y = 1 \\ \frac{1}{2} y = 1 - x \\ y = 2(1 - x) \\ y = 2 - 2x$

By substituting the value of y = (2 - 2x) in Equation 1

$\frac{3}{2} x - y = \frac{1}{4} \\ \frac{3}{2}x - (2 - 2x) = \frac{1}{4} \\ \frac{3}{2} x - 2 + 2x = \frac{1}{4 } \\ \frac{3}{2} x + 2x = \frac{1}{4} + 2 \\ \frac{3x + 4x}{2} = \frac{1 + 8}{4} \\ \frac{7x}{2} = \frac{9}{4 } \\ 7x = \frac{9 \times 2}{4} \\ 7x = \frac{18}{4} \\ 7x = \frac{9}{2} \\ x = \frac{9}{14}$

By substituting value of x in (y = 2 - 2x)

$y = 2 - 2x \\ = 2 - (2 \times \frac{9}{14} ) \\ = 2 - \frac{9}{7} \\ = \frac{14 - 9}{7} \\ = \frac{5}{7}$

Hence,

$x = \frac{9}{14} \: and \: y = \frac{5}{7}$

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