The equation of a line is called a linear equation. The equation of a parabola is called a quadratic equation; a quadratic equation has at least one variable squared. Together, the two equations form a System. In these worksheets, students will learn how to solve linear quadratic systems algebraically to find the solution set. Students may find that they need extra paper to have enough room for their work. Answers may be both positive and negative numbers. This set of worksheets contains step-by-step solutions to sample problems, both simple and more complex problems, ample problems for independent practice, reviews, and quizzes. When finished with this set of worksheets, students will be able to solve linear quadratic systems algebraically.

We all know what linear systems are, where the highest power in the equation is 1, and what quadratic systems are, ones where the highest power is 2. Linear systems appear as straight lines on a graph, and quadratic systems form a parabolic curve on the graph. That is everything that we know, but what about linear-quadratic systems? What do we know about these? Well, linear-quadratic systems are those which contain one linear equation and one quadratic equation. There are three possible situations when you graph a linear-quadratic system. The first is when a linear graph intersects the parabola of a quadratic equation at two points. This gives two solutions. The second one is where the linear line is tangent to the parabola. This system has one solution. The third situation is when the linear line and the parabola never meet, and this type of system has no solution. These worksheets explain how to work with linear quadratic systems. Sample problems are solved and practice problems are provided.