Question

3x-5y=4 9x-2y=7 substitution methof

Answer 1

Correct Question

3x - 5y = 4

9x - 2y = 7

Solve the equations using substitution method.

Answer

$\sf \dashrightarrow 3x - 5y = 4 \: \: --- (i)$

$\sf \dashrightarrow 9x - 2y = 7 \: \: --- (ii)$

By first equation,

$\sf \dashrightarrow 3x - 5y = 4$

$\sf \dashrightarrow 3x = 4 + 5y$

$\sf \dashrightarrow x = \dfrac{4 + 5y}{3}$

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

$\sf \dashrightarrow 9x - 2y = 7 \: \: --- (i)$

$\sf \dashrightarrow 9 \bigg( \dfrac{4 + 5y}{3} \bigg) - 2y = 7$

$\sf \dashrightarrow \dfrac{36 + 45y}{3} - 2y = 7$

$\sf \dashrightarrow \dfrac{36 + 45y - 6y}{3} = 7$

$\sf \dashrightarrow \dfrac{36 + 39y}{3} = 7$

$\sf \dashrightarrow 36 + 39y = 7 \times 3$

$\sf \dashrightarrow 36 + 39y = 21$

$\sf \dashrightarrow 39y = 21 - 36$

$\sf \dashrightarrow 39y = -15$

$\sf \dashrightarrow y = \dfrac{-15}{39}$

$\sf \dashrightarrow y = \dfrac{-5}{13}$

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

$\sf \dashrightarrow 3x - 5 \bigg( \dfrac{-5}{13} \bigg) = 4$

$\sf \dashrightarrow 3x + \dfrac{25}{13} = 4$

$\sf \dashrightarrow \dfrac{39x + 25}{13} = 4$

$\sf \dashrightarrow 39x + 25 = 13 \times 4$

$\sf \dashrightarrow 39x + 25 = 52$

$\sf \dashrightarrow 39x = 52 - 25$

$\sf \dashrightarrow 39x = 27$

$\sf \dashrightarrow x = \dfrac{27}{39}$

$\sf \dashrightarrow x = \dfrac{9}{13}$

Hence, the values of x and y are -5/13 and 9/13 respectively.