Answer:
[tex]x=\frac{7}{2} =3.5\\\\y=2[/tex]
Step-by-step explanation:
The addition method (elimination method) allows us to combine two equations in such a way that the resulting equation has only one variable. Then we can use simple algebraic methods to solve that variable
Let:
[tex]4x-6y=2\hspace{10}(1)\\\\and\\\\2x-y=5\hspace{15}(2)[/tex]
Let's multiply (2) by -2:
[tex]-2*(2):\\\\2x(-2)-y(-2)=5(-2)\\\\-4x+2y=-10\hspace{12}(-2*(2))[/tex]
Now, add (1) and (-2*(2)):
[tex](1)+(-2*(2)):\\\\4x+(-4x)-6y+(2y)=2+(-10)\\\\-4y=-8[/tex]
Hence, solving for y:
[tex]y=\frac{-8}{-4} =2[/tex]
Replacing y into (2):
[tex]2x-(2)=5[/tex]
Solving for x:
[tex]2x=5+2\\\\2x=7\\\\x=\frac{7}{2} =3.5[/tex]
Therefore:
[tex]x=\frac{7}{2} =3.5\\\\y=2[/tex]
