Question

solve 3x-5y=5 and 9x-2y=7 by substitution method​

Answer 1

Answer:

The ans is in above photo step by step

Answer 2

SolutioN :

We have, Pair of Linear Equation.

$\tt \dagger \: \: \: \: \: 3x - 5y = 5. \: \: \: \: \: - (1)$

$\tt \dagger \: \: \: \: \: 9x - 2y = 7. \: \: \: \: \: - (2)$

Now, Let's solve Equation by Substitution method.

Taking Equation ( 1 )

$\tt : \implies 3x - 5y = 5.$

$\tt : \implies 3x = 5 + 5y.$

$\tt : \implies x = \dfrac{ 5 + 5y}{3}. \: \: \: \: \: - (3)$

Now, Putting the value of x in Equation ( 2 ) We get.

$\tt : \implies 9x - 2y = 7.$

$\tt : \implies 9 \times \dfrac{5 + 5y}{3} - 2y = 7.$

$\tt : \implies \cancel9 \times \dfrac{5 + 5y}{ \cancel3} - 2y = 7.$

$\tt : \implies 3 \times(5 + 5y) - 2y = 7.$

$\tt : \implies 15 + 15y - 2y = 7.$

$\tt : \implies 13y = - 8.$

$\tt : \implies y = - \dfrac{8}{13}$

Now, Putting the value of y = -8/13. in Equation ( 3 )

$\tt : \implies x = \dfrac{ 5 + 5y}{3}$

$\tt : \implies x = \dfrac{ 5 + 5\Big( - \dfrac{8}{13} \Big)}{3}.$

$\tt : \implies x = \dfrac{ \dfrac{65- 40}{13} }{ \dfrac{3}{1} }$

$\tt : \implies x = \dfrac{25}{13} \times \dfrac{1}{3}$

$\tt : \implies x = \dfrac{ 2 5}{39}$

Therefore,the value of x = 25 /39 and y = - 8/13.