Question

How do you use the substitution method to solve 3x-15y=-12 and 3x+24y=-12?

Answer 1

Answer;

$3x - 15y = - 12.....(i) \\ 3x + 24y = - 12....(ii)$

Solving for eqⁿ (i),

$3x - 15y = - 12 \\ \\ 15y = 3x + 12 \\ \\ y = \frac{3x + 12}{15}$

Putting the value of y in (ii),

$3x + 24y = - 12 \\ \\ 3x + \cancel{24} \: {}^{8} ( \frac{3x + 12}{ \cancel{15} \: _5 }) = - 12 \\ \\ 3x + \frac{24x + 96}{5} = - 12 \\ \\ \frac{15x + 24x + 96}{5} = - 12 \\ \\ 39x + 96 = - 60 \\ \\ 39x = - 60 - 96 \\ \\ 39x = - 156 \\ \\ x = \frac{ - 156}{39} \\ \\ \boxed{ \fcolorbox{red}{yellow}{ \bf x = - 4}}$

Substituting the value of x in (i),

$3x - 15y = - 12 \\ \\ 3( - 4) - 15y = - 12 \\ \\ - 12 - 15y = - 12 \\ \\ 15y = - 12 + 12 \\ \\ \boxed{ \fcolorbox{red}{yellow}{ \bf y = 0}}$

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