Answer:
The y-coordinate is [tex]y=-\frac{8}{13}[/tex]
Step-by-step explanation:
Given equations are
[tex]5x=y+6\hfill (1)[/tex]
[tex]2x-3y=4\hfill (2)[/tex]
To solve the given equations by substitution method
From Equation (1) we can write [tex]x=\frac{y+6}{5}[/tex]
Substitute the value [tex]x=\frac{y+6}{5}[/tex] in equation (2) we get
[tex]2\times (\frac{y+6}{5})-3y=4[/tex]
[tex]\frac{2}{5}(y+6)-3y=4[/tex]
[tex]\frac{2y+12}{5}-3y=4[/tex]
[tex]\frac{2y+12-15y}{5}=4[/tex]
[tex]-13y+12=20[/tex]
[tex]-13y=20-12[/tex]
Therefore [tex]y=-\frac{8}{13}[/tex]
Substitute the value of [tex]y=-\frac{8}{13}[/tex] in equation (1) we get
[tex]5x=-\frac{8}{13}+6[/tex]
[tex]x=-\frac{8-78}{-65}[/tex]
[tex]=\frac{70}{65}[/tex]
Therefore [tex]x=\frac{14}{13}[/tex]
Therefore the y-coordinate is [tex]y=-\frac{8}{13}[/tex]
