Question

Solve each of the following system of equations by the method of substitution. 2x=3y ; 2x+3y=60​

Answer 1

Answer

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

$\sf \dashrightarrow 2x + 3y = 60 \: \: --- (ii)$

By first equation,

$\sf \dashrightarrow 2x = 3y$

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

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

$\sf \dashrightarrow 2x + 3y = 60$

$\sf \dashrightarrow 2 \bigg( \dfrac{3y}{2} \bigg) + 3y = 60$

$\sf \dashrightarrow \dfrac{6y}{2} + 3y = 60$

$\sf \dashrightarrow \dfrac{6y + 6y}{2} = 60$.$\sf \dashrightarrow \dfrac{12y}{2} = 60$

$\sf \dashrightarrow \dfrac{6y}{1} = 60$

$\sf \dashrightarrow 6y = 60 \times 1$

$\sf \dashrightarrow 6y = 60$

$\sf \dashrightarrow y = \dfrac{60}{6}$

$\sf \dashrightarrow y = 10$

Now, we can find the value of x by first equation.

$\sf \dashrightarrow 2x = 3y$

$\sf \dashrightarrow 2x = 3(10)$

$\sf \dashrightarrow 2x = 30$

$\sf \dashrightarrow x = \dfrac{30}{2}$

$\sf \dashrightarrow x = 15$

Hence, the values of x and y are 15 and 10 respectively.