This week in math we learned how to solve systems algebraically when one is a linear system and the other quadratic using substitution. We learned about this method in Math 10. As a refresher, substitution is when you substitute one equation into the other and put the found variables into the original equation to find the other variables.

The first step when using substitution is to isolate one of the variables in one of the equations and put it into the other equation where the respective variable is. From here, you can simplify the equation and make everything on one side equal to zero. Next, factor it to find the intercepts, or in other words, solutions to the variable. Once you have the solutions, put the first solution into the original equation you isolated the variable in, and solve to find the variable. These will be your two variables for the first point. Do the same with the other solution you found and once you’ve found the other variable, these will be your two variables for the second point. I’ve included an example of a system solved using substitution, refer to this as you read these directions.