What's the difference between "Linear Combination," and the "Substitution Method," and how do I solve using Substitution?

Question

anonymous · Answer

for substitution you express one variable through another.
For combination (elimination) you eliminate one variable.

anonymous · Answer

To solve using the substitution method, we rewrite one equation and sub it into the other.

For example 4x + 3y = (-2)     [1]
                    3x + 2y = (-3)     [2]

Let rewrite [1] so y is our subject

4x+3y=-2 
    3y=-2-4x
       y=-2/3-(4/3)x

Now that we have y sub this into the second equation and solve for x

3x+2(-2/3-(4/3)x)=-3
3x-4/3-8/3 x=-3
             1/3 x=-5/3
                    x=-5
                     
Now sub x=-5 into our rearranged y equation

y=-2/3-(4/3)*(-5)
  =-2/3+20/3
  =6

So y=6 and x=-5