Question

solve by substitution method 2x/y+2-6/7=0 and x+2/2y=1/2​

Answer 1

Question -

Solve the following pair of equations by substitution method -

$\frac{2x}{y + 2} - \frac{6}{7} = 0$

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

Solution -

$\frac{2x}{y + 2} - \frac{6}{7} = 0$

$\frac{2x}{y + 2} = \frac{6}{7} ......1)$

And,

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

By cross multiplying -

$2(x + 2) = 2y$

$2x + 4 = 2y$

$2x = 2y - 4..........2)$

Putting the value of 2x in equation 1) we will get -

$\frac{2y - 4}{y + 2} = \frac{6}{7}$

By cross multiplying -

$7(2y - 4) = 6(y + 2)$

$14y - 28 = 6y + 12$

$14y - 6y = 12 + 28$

$8y = 40$

$y = \frac{40}{8}$

$y = 5$

Now,

Substituting the value of y in equation 2) we will get -

$2x = 2 \times 5 - 4$

$2x = 10 - 4$

$2x = 6$

$x = \frac{6}{2}$

$x = 3$

Verification -

$\frac{2x}{y + 2} - \frac{6}{7} = 0$

Putting the values of x and y

$\frac{2 \times 3}{5 + 2} - \frac{6}{7} = 0$

$\frac{6}{7} - \frac{6}{7} = 0$

$0 = 0$

Also,

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

$\frac{3 + 2}{2 \times 5} = \frac{1}{2}$

$\frac{5}{10} = \frac{1}{2}$

$\frac{1}{2} = \frac{1}{2}$

L. H. S =R. H. S

Verified

Therefore the value of x is 3 and y is 5

Answer 2

Answer:

Hence x=2 and y=14/5

I hope this helps you