Question

solve the equations
$x \div 2 - y \div 5 = 4 \\ x \div 7 + y \div 15 = 3$
​

Answer 1

hence the solution for above problem is here x=14. and y =15

Answer 2

Question:

To Solve the equation :

$\sf \star \:\:\frac{x}{2} - \frac{y}{5} = 4 \\\\\star\sf \:\:\frac{x}{7} + \frac{y}{15} = 3$

Solution:

Let ,

$\sf \star \:\:\frac{x}{2} - \frac{y}{5} = 4\:\:\:\:…(i) \\\\\star\sf \:\:\frac{x}{7} + \frac{y}{15} = 3\:\:\:\:…(ii)$

Solving (i)

$\bf \star \:\:\frac{x}{2} - \frac{y}{5} = 4\:\:\:\:…(i) \\ \\ \sf\implies \frac{5x-2y}{10} = 4 \\ \\\implies\sf \blue{5x -2y=40}\:\:\:\:…(iii)$

Solving (ii)

$\star\bf \:\:\frac{x}{7} + \frac{y}{15} = 3 \:\:\:\:…(ii) \\\\\implies\sf \frac{15x-7y}{105} = 3 \\\\\implies\sf \blue{15x-7y= 315}\:\:\:\: …(iv)$

Multiply (iii) by 3.

$\implies\sf \red 3 \times ({5x -2y=40})\:\:\:\: …(iii) \\ \implies \sf 15x-6y=120 \:\:\:…(v)$

Subtract (v) from (iv)

$\sf 13y = 195 \\\\ ::\implies \boxed{\pink{y=15}}$

Put the value in y in (iii)

$\implies\sf 5x -2y=40 \:\:\:…(iii) \\\\\implies\sf 5x-2(15)=40 \\ \\ \implies\sf 5x-30=40 \\\\\implies\sf 5x=70 \\ \\::\implies \boxed{\pink{x=14}}$

Therefore,

Value of x is 14 and y is 15.