Question

solve the syatem using the substitution method

4x - 5y = - 3
-x + 2y = 3

Answer 1

Using the substitution method means you first find one of the two variables (perhaps in terms of the other variable) and then 'substitute' this result in the other equation. If we apply it on this system we would work as follows:

1) Look at the second equation. You can easily rewrite this to:
x = 2y-3
So now you have x in terms of y

2) You now simple replace every x in the first equation with result you got from the second equation, meaning:

4x - 5y= -3
<=> 4(2y-3) - 5y = -3
<=> (8y - 12) - 5y = -3
<=> 3y = 9
<=> y = 3

3) Now that we have found that y equals 3, we can replace y with 3 in the second equation. We then find that:

x = 2y-3
<=> x = 2*3 - 3
<=> x = 3

So, the solution of this system is:
x=y=3