Question

solve the following by substitution method :- i) 3x -5y =19 , -7x + 3y = -1​

Answer 1

Answer

$\sf \dashrightarrow 3x - 5y = 19 \: \: --- (i)$

$\sf \dashrightarrow -7x + 3y = -1 \: \: --- (ii)$

By first equation,

$\sf \dashrightarrow 3x - 5y = 19$

$\sf \dashrightarrow 3x = 19 + 5y$

$\sf \dashrightarrow x = \dfrac{19 + 5y}{3}$

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

$\sf \dashrightarrow -7x + 3y = -1$

$\sf \dashrightarrow -7 \bigg( \dfrac{19 + 5y}{3} \bigg) + 3y = -1$

$\sf \dashrightarrow \dfrac{-133 + (-35y)}{3} + 3y = -1$

$\sf \dashrightarrow \dfrac{-133 - 35y}{3} + 3y = -1$

$\sf \dashrightarrow \dfrac{-133 - 35y + 9y}{3} = -1$

$\sf \dashrightarrow \dfrac{-133 - 26y}{3} = -1$

$\sf \dashrightarrow -133 - 26y = -1 \times 3$

$\sf \dashrightarrow -133 - 26y = -3$

$\sf \dashrightarrow -26y = -3 + 133$

$\sf \dashrightarrow -26y = 130$

$\sf \dashrightarrow y = \dfrac{130}{-26}$

$\sf \dashrightarrow y = -5$

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

$\sf \dashrightarrow 3x - 5y = 19$

$\sf \dashrightarrow 3x - 5(-5) = 19$

$\sf \dashrightarrow 3x - (-25) = 19$

$\sf \dashrightarrow 3x + 25 = 19$

$\sf \dashrightarrow 3x = 19 - 25$

$\sf \dashrightarrow 3x = -6$

$\sf \dashrightarrow x = \dfrac{-6}{3}$

$\sf \dashrightarrow x = -2$

Hence, the values of x and y are -2 and -5 respectively.