Question

Solve this equation using substitution method

$\frac{x}{7} + \frac{y}{3} = 5 \\ \frac{x}{2} - \frac{y}{9} = 6$

Answer 1

$\frac{x}{7} + \frac{y}{3} = 5 \\ \frac{3x + 7y}{21} = 5 \\ 3x + 7y = 105 \: \: \: \: \: \: \: \: eq1$
$\frac{x}{2} - \frac{y}{9} = 6 \\ \frac{9x - 2y}{18} = 6 \\ 9x - 2y = 108 \: \: \: \: \: \: eq2 \\ - 2y = 108 - 9x \\ 2y = -108 + 9x \\ y = \frac{-108 + 9x}{2} \: \: \: \: put \: into \: eq \: 1$
$3x + 7( \frac{-108 +9x }{2} ) = 105 \\ \frac{6x - 756 + 63x}{2} = 105 \\ 69x - 756 = 210 \\ 69x = 210 + 756 \\ 69x = 966 \\ x = \frac{966}{69} \\x=14\\ 3(14)+7y=105\\ 42+7y=105\\ 7y=105-42\\ 7y=63\\ y=9$