Question

(iv) 0.2x +0.3y=1.3
0.4x +0.5y=2.3 solve by substitution method plz​

Answer 1

Answer

$\sf \dashrightarrow 0.2x + 0.3y = 1.3 \: \: --- (i)$

$\sf \dashrightarrow 0.4x + 0.5y = 2.3 \: \: --- (ii)$

By multiplying both equations by 10,

$\sf \dashrightarrow 2x + 3y = 13$

$\sf \dashrightarrow 4x + 5y = 23$

By first equation,

$\sf \dashrightarrow 2x + 3y = 13$

$\sf \dashrightarrow 2x = 13 - 3y$

$\sf \dashrightarrow x =\dfrac{13 - 3y}{2}$

Now, let's find the value of y by second equation.

$\sf \dashrightarrow 4x + 5y = 23$

$\sf \dashrightarrow 4 \bigg( \dfrac{13 - 3y}{2} \bigg) + 5y = 23$

$\sf \dashrightarrow \dfrac{52 - 12y}{2} + 5y = 23$

$\sf \dashrightarrow \dfrac{52 - 12y + 10y}{2} = 23$

$\sf \dashrightarrow \dfrac{52 - 2y}{2} = 23$

$\sf \dashrightarrow 52 - 2y = 23 \times 2$

$\sf \dashrightarrow 52 - 2y = 46$

$\sf \dashrightarrow -2y = 46 - 52$

$\sf \dashrightarrow -2y = -6$

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

$\sf \dashrightarrow y = 3$

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

$\sf \dashrightarrow 2x + 3y = 13$

$\sf \dashrightarrow 2x + 3(3) = 13$

$\sf \dashrightarrow 2x + 9 = 13$

$\sf \dashrightarrow 2x = 13 - 9$

$\sf \dashrightarrow 2x = 4$

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

$\sf \dashrightarrow x = 2$

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