Question

Solve the following system of equations by the substitution method.

Answer 1

Answer:

The y-coordinate is $y=-\frac{8}{13}$

Step-by-step explanation:

Given equations are

$5x=y+6\hfill (1)$

$2x-3y=4\hfill (2)$

To solve the given equations by substitution method

From Equation (1) we can write $x=\frac{y+6}{5}$

Substitute the value $x=\frac{y+6}{5}$ in equation (2) we get

$2\times (\frac{y+6}{5})-3y=4$

$\frac{2}{5}(y+6)-3y=4$

$\frac{2y+12}{5}-3y=4$

$\frac{2y+12-15y}{5}=4$

$-13y+12=20$

$-13y=20-12$

Therefore $y=-\frac{8}{13}$

Substitute the value of $y=-\frac{8}{13}$ in equation (1) we get

$5x=-\frac{8}{13}+6$

$x=-\frac{8-78}{-65}$

$=\frac{70}{65}$

Therefore $x=\frac{14}{13}$

Therefore the y-coordinate is $y=-\frac{8}{13}$