# How to solve quadratic linear systems of equations algebraically

A Quadratic Equation is the equation of a parabola and has at least one variable squared such as x 2 And together they form a System of a Linear and a Quadratic Equation. Permutations Combinations Factorials Quiz:

Using equation 1. The solution consists of the four ordered pairs. If these equations were graphed, these ordered pairs would represent the points of intersection of the graphs.

This system is more easily solved using substitution. Solve equation 2 for x; then substitute that result for x in equation 1. Solving equation 2 for x. Substituting into equation 1.

Using equation 2. The solution consists of the two ordered pairs.

## Systems of Equations Solved Algebraically

If this system of equations were graphed, these two points would represent the points where the graphs would intersect. Removing book from your Reading List will also remove any bookmarked pages associated with this title. Are you sure you want to remove bookConfirmation and any corresponding bookmarks?

Systems of Equations Solved Algebraically. Formulas Absolute Value Equations Quiz: Linear Inequalities Compound Inequalities Quiz: Distance Formula Midpoint Formula Quiz: Greatest Common Factor Quiz: Square Trinomials Factoring by Regrouping Quiz: Function Notation Compositions of Functions Quiz: Algebra of Functions Quiz: Basic Definitions Inverse Functions Quiz: Inverse Functions Polynomial Functions Quiz: Remainder Theorem Factor Theorem Quiz: Factor Theorem Zeros of a Function Quiz: Solve this linear-quadratic system of equations algebraically and check your solution: Solve for one of the variables in the linear equation.

**The elimination method for solving linear systems**

Substitute this value into the quadratic equationand solve the resulting equation. You now have TWO values for x.

This tells you that there may be two possible solutions. Find the corresponding values for y. Substitute each value into the linear equation in place of x.

### Systems of Linear and Quadratic Equations

You now have ONE value for x. This tells you that there may be only one solution. Find the corresponding value for y. Substitute the value into the linear equation in place of x.