Section 6.3 Solving a System of Equations: Elimination
Example 6.10.
Let's say we want to solve the following system of equations:
Remember that the symbol
Notice what happened: the
Now we have our answer of
Checkpoint 6.11.
Solve the following system of equations using elimination:
We want to start by adding the equations together. In other words, we are going to add
Now that we have our answer for
So we have our final answer:
After you find the value for one variable, plug it into both starting equations and make sure they give you the same value for the second variable
After you have your final answer, plug the point into both starting equations and make sure it works for both
Example 6.12.
Suppose we want to solve the following system of equations:
We have a couple of choices here:
If we multiply both sides of the second equation by
then we would be able to cancel the 'sIf we multiply the second equation by
then we would be able to cancel the 's.
It doesn't matter which one we choose, so let's go with the first option for this example. When we multiply the second equation by
Now, we add that to the first equation:
Now we will plug
Therefore, we have our answer:
Checkpoint 6.13.
Solve the following system using elimination.
We have a couple of choices here:
If we multiply both sides of the first equation by
then we would be able to cancel the 'sIf we multiply the second equation by
then we would be able to cancel the 's.
It doesn't matter which one we choose, so let's go with the second option for this exercise. When we multiply the second equation by
Now, we add that to the first equation:
Now we will plug
Therefore, we have our answer: