Answer:
The answer is:
[tex]x=\frac{75}{13} \\\\y=\frac{35}{13}[/tex]
Step-by-step explanation:
Given:
x=4y-5
2x+5y=25
Now, to solve the systems of equations.
[tex]x=4y-5\ \ \ ..........(1)[/tex]
[tex]2x+5y=25\ \ \ .......(2)[/tex]
Now, to solve by using substitution:
[tex]2x+5y=25[/tex]
Substituting the value of [tex]x[/tex] from equation (1) we get:
[tex]2(4y-5)+5y=25\\\\8y-10+5y=25\\\\13y-10=25[/tex]
Adding both sides by 10 we get:
[tex]13y=35[/tex]
Dividing both sides by 13 we get:
[tex]y=\frac{35}{13}[/tex]
Now, substituting the value of [tex]y[/tex] in equation (1):
[tex]x=4y-5[/tex]
[tex]x=4\times (\frac{35}{13}) -5\\\\x=\frac{140}{13} -5[/tex]
[tex]x=\frac{140-65}{13} \\\\x=\frac{75}{13}[/tex]
Therefore, the answer is:
[tex]x=\frac{75}{13} \\\\y=\frac{35}{13}[/tex]