Question

Solve using substitution method: X= y/3 +2 7x − 5y = 10 Solve for (x,y)

Answer 1

$\quad \huge \quad \quad \boxed{ \tt \:Answer }$

$\qquad \tt \rightarrow \:x = 5/2$

$\qquad \tt \rightarrow \: y = 3/2$

____________________________________

$\large \tt Solution \: :$

$\qquad \tt \rightarrow \: x = \cfrac{y}{3} + 2 \: \: \: \: \: \: \: \: - (1)$

$\qquad \tt \rightarrow \: 7x -5 y = 10 \: \: - (2)$

$\textsf{put value of x in equation 2}$

$\qquad \tt \rightarrow \: 7 \bigg( \cfrac{y}{3} + 2 \bigg) - 5y = 10$

$\qquad \tt \rightarrow \: \cfrac{7y}{3} + 14 - 5y = 10$

$\qquad \tt \rightarrow \: \cfrac{7y}{3} - 5y = 10 - 14$

$\qquad \tt \rightarrow \: \cfrac{7y - 15y}{3} = - 4$

$\qquad \tt \rightarrow \: - 8y = - 4(3)$

$\qquad \tt \rightarrow \: y = \cfrac{ - 12}{ - 8}$

$\qquad \tt \rightarrow \: y = \cfrac{ 3}{ 2}$

$\textsf{put value of y in equation 1 }$

$\qquad \tt \rightarrow \: x = \cfrac{y}{3} + 2$

$\qquad \tt \rightarrow \: x = \bigg (\cfrac{3}{2} \sdot\cfrac{1}{3} \bigg) + 2$

$\qquad \tt \rightarrow \: x = \cfrac{1}{2} + 2$

$\qquad \tt \rightarrow \: x = \cfrac{1 + 4}{2}$

$\qquad \tt \rightarrow \: x = \cfrac{5}{2}$