Question

Solving 3x+5y=1 and 2x-y=3 using substitution method

Answer 1

3x + 5y = 1 -------(i)
2x - y = 3 -------(ii)

From (i)

3x + 5y = 1

=> 3x = 1- 5y

=> x = $\frac{1 - 5y}{3}$ ------(iii)



Substituting (iii) in (ii)

2x -y = 3

=> 2 × $\frac{1 - 5y}{3}$ - y = 3

=> $\frac{2 - 10y}{3}$ - y = 3

=> $\frac{2 - 10y - 3y}{3}$ = 3

=> $\frac{2 -13y}{3}$ = 3

=> 2 - 13y = 9

=>-13y = 9 -2

=> y = $\frac{-7}{13}$



From (iii)

x = $\frac{1 - 5 \times (\frac{ - 7}{13}) }{3}$

= $\frac{1 + \frac{35}{13} }{3}$

=$\frac{ \frac{13 + 35}{13} }{3}$

= $\frac{13 + 35}{13 × 3}$

= $\frac{48}{39}$

= $\frac{16}{13}$


$\huge{x = \frac{16}{13} } \\ \\ \huge{y = \frac{ - 7}{13} }$