What does it mean to solve a system of equations by substitution?
I think that this is better explained with an example.
Lets say that we have the linear system
Neither one of these equation can be solved on their own because an equation with more than one unknown value cannot be solved.
We have to eliminate one of the variable by substitution.
We have 2 options. First, pick one of equations and then solve for either
Lets use the first equation and solve for
Now we see that
Make substitution for
Combine like terms
Subtract 17 from both sides
Divide by sides by
Now we can find
Okay, so now we know that
We check our work by substituting those values into the other equation.