Question

Solve the following system of equations by the substitution method.

Answer 1

5x = y + 6 (I)
2x - 3y = 4 (II)
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We have:
5x = y + 6 → $x = \frac{y+6}{5}$

Soon:
2x - 3y = 4 → $2* (\frac{y+6}{5}) - 3y = 4\to \frac{2y+12}{5} - 3y = 4$
least common multiple (5)
$\frac{2y+12}{5} - 3y = 4\to \frac{2y+12}{\diagup\!\!\!\!\!5} - \frac{15y}{\diagup\!\!\!\!\!5} = \frac{20}{\diagup\!\!\!\!\!5}$
$2y + 12 - 15y = 20$
$- 15y + 2y = 20 - 12$
$- 13y = 8$
$\boxed{\boxed{y = - \frac{8}{13} }}\end{array}}\qquad\quad\checkmark$