Question

solve the following pair of equations by substitution method. 7x-15y 2 and x+2y 3

Answer 1

x+2y=3
x=3-2y......(.1)

put this in 7x-15y=2

21-14y-15y=2
-29y=-19
y=19/29

Answer 2

Answer:

$7x - 15y = 2 \\ \: \implies7x = 2 + 15y \\ \implies \: x = \frac{2 + 15y}{7} \: \: \: \: \: \rightarrow(i) \\ \\ x + 2y = 3 \\ \implies\frac{2 + 15y}{7} + 2y = 3 \: (putting \: x = \frac{2 + 15y}{7} ) \\ \implies \frac{2 + 15y + 14y}{7} = 3 \\ \implies15y + 14y = 3 \times 7 - 2 \\ \implies29y = 21 - 2 \\ \implies \: y = \frac{19}{29} \\ \\ \\ \: \: substituting \: the \: value \: of \: y \: in \: equation \: (i) \\ 7x - 15 \times \frac{19}{29} = 2 \\ \implies7x - \frac{285}{29} = 2 \\ \implies7x = 2 + \frac{285}{29} \\ \implies7x = \frac{58 + 285}{29} \\ \\ \: \implies7x = \frac{343}{29 } \\ \\ \implies \: x = \frac{343}{203} \\ \\ \implies \: x = \frac{49}{29} \\ \\ \therefore \: x = \frac{49}{29} \\ \\ y = \frac{19}{29}$