Question

solve for x and y :

10x + 3y = 75
6x - 5y = 11​

Answer 1

Given :

• 10x + 3y = 75
• 6x - 5y = 11

To Find :

• Value of x and y = ?

Solution :

The given equations are :

• 10x + 3y = 75 - (i)
• 6x - 5y = 11 - (ii)

From equation (i), we have :

$: \sf \implies 10x + 3y = 75 \\ \\ : \sf \implies 10x = 75 - 3y \\ \\ : \sf \implies x = \dfrac{75 - 3y}{10}$

Now, substitute this in equation (ii) :

$\sf : \implies 6 \bigg(\dfrac{75 - 3y}{10} \bigg) - 5y = 11 \\ \\ \sf : \implies \cancel{6} \bigg(\dfrac{75 - 3y}{\cancel{10}} \bigg) - 5y = 11 \\ \\ \sf : \implies 3 \bigg(\dfrac{75 - 3y}{5} \bigg) - 5y = 11 \\ \\ \sf : \implies \dfrac{225 - 9y}{5} - 5y = 11 \\ \\ \sf : \implies \dfrac{225 - 9y}{5} - \dfrac{25y}{5} = 11 \\ \\ \sf : \implies \dfrac{225 - 9y - 25y}{5} = 11 \\ \\ \sf : \implies 225 - 34y = 11 \times 5 \\ \\ \sf : \implies 225 - 34y = 55 \\ \\ \sf : \implies - 34y = 55 - 225 \\ \\ \sf : \implies - 34y = - 170 \\ \\ \sf : \implies 34y = 170 \\ \\ \sf : \implies y = \cancel{\dfrac{170}{34}} \\ \\\sf : \implies y = 5 \\ \\ \underline{ \boxed{ \bf \therefore \: y = 5}}$

Now, substitute y = 5 in equation (i) :

$\sf : \implies 10x + 3(5) = 75 \\ \\ \sf : \implies 10x + 15 = 75 \\ \\ \sf : \implies 10x = 75 - 15 \\ \\ \sf : \implies 10x = 60 \\ \\ \sf : \implies x = \cancel{\dfrac{60}{10}} \\ \\ \sf : \implies x = 6 \\ \\ \underline{ \boxed{ \bf \therefore \: x \: = 6}}$

Hence, value of :

• x = 6
• y = 5

Answer 2

Answer

x = 6 and y = 5 is right answer