Question

solve the following by substitution method :-
i) 2x + 3y =5 , 3x + 4y = 6​

Answer 1

Answer

$\sf \dashrightarrow 2x + 3y = 5 \: \: --- (i)$

$\sf \dashrightarrow 3x + 4y = 6 \: \: --- (ii)$

By first equation,

$\sf \dashrightarrow 2x + 3y = 5$

$\sf \dashrightarrow 2x = 5 - 3y$

$\sf \dashrightarrow x = \dfrac{5 - 3y}{2}$

Now, we can find the value of y by second equation.

$\sf \dashrightarrow 3x + 4y = 6$

$\sf \dashrightarrow 3 \bigg( \dfrac{5 - 3y}{2} \bigg) + 4y = 6$

$\sf \dashrightarrow \dfrac{15 - 9y}{2} + 4y = 6$

$\sf \dashrightarrow \dfrac{15 - 9y + 8y}{2} = 6$

$\sf \dashrightarrow \dfrac{15 - 1y}{2} = 6$

$\sf \dashrightarrow 15 - 1y = 6 \times 2$

$\sf \dashrightarrow 15 - 1y = 12$

$\sf \dashrightarrow -1y = 12 - 15$

$\sf \dashrightarrow -1y = -3$

$\sf \dashrightarrow y = \dfrac{-3}{-1}$

$\sf \dashrightarrow y = 3$

Now, let's find the value of x by first equation.

$\sf \dashrightarrow 2x + 3y = 5$

$\sf \dashrightarrow 2x + 3(3) = 5$

$\sf \dashrightarrow 2x + 9 = 5$

$\sf \dashrightarrow 2x = 5 - 9$

$\sf \dashrightarrow 2x = -4$

$\sf \dashrightarrow x = \dfrac{-4}{2}$

$\sf \dashrightarrow x = -2$

Hence, the values of x and y are -2 and 3 respectively.