How do I do this? solve the system using substitution.
2x = y – 4
− 3y = x − 5

Question

How do I do this? solve the system using substitution.
2x = y – 4
− 3y = x − 5

owlcoffee · Answer

So we have:
$$2x=y-4$$
$$-3y=x-5$$
Now, there are various methods to solve this system of equations but we are asked to use the "substitution".
Now, this methos consists in solving one of the equations for any variable and replace it on the other equation. Sounds a little confusin, I know, but let's give it a try.
i'll take the first equation, and try to leave the x on it's own, ending with:
$$x=\frac{ y-4 }{ 2 }$$
Now, let's take that equality we just found, and replace it on the second equation:
$$-3y=(\frac{ y-4 }{ 2 })-5$$
Look at that, we've just transformed a 2 variable equation into an equation with only one variable, this is the whole point of the "substitution" method.
Doing a little algebra, doing common denominator and multiplying by 2.
$$-6y=y-4-10$$
Let's solve it for y:
$$-7y=-14$$
$$y=2$$
Now, we have found the value of "y", let's take te equation that determined the value of x, and replace the value we just found:
$$x=\frac{ y-4 }{ 2 } , y=2$$
$$x=\frac{ 2-4 }{ 2 }$$
$$x=-1$$
So we can conclude that the solution is:
$$y=2$$
$$x=1$$