# Systems of linear and quadratic equations

## How Do You Solve a System of Equations Using Substitution if One Equation is a Quadratic?

How to solve a simultaneous quadratic and linear equation

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Just like a system of linear equations means 'more than 1 line ' on a graph see picture on right ,. It is just a line and a parabola together on the same graph! The solution is where the equations 'meet' or intersect. The red point on the right is the solution of a system of linear equations. The same thing is true for a linear quadratic system. The solution is where the parabola and the line 'meet'. A system of a linear equation and a quadratic equation can have one real solution , two real solutions or no real solutions.

In earlier chapters we've shown you how to solve quadratic equations by factoring. A quadratic equation as you remember is an equation that can be written on the standard form. You know by now how to solve a quadratic equation using factoring. Another way of solving a quadratic equation is to solve it graphically. The roots of a quadratic equation are the x-intercepts of the graph. Graph the equation. This could either be done by making a table of values as we have done in previous sections or by computer or a graphing calculator.

Systems of Linear and Quadratic Equations And together they form a System A System of those two equations can be solved (find where they intersect).
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A quadratic equation is defined as an equation in which one or more of the terms is squared but raised to no higher power. In a linear- quadratic system where only one variable in the quadratic is squared, the graphs will be a parabola and a straight line. When graphing a parabola and a straight line on the same set of axes, three situations are possible. When prompted for the "First curve? Hit Enter.

Be sure to use a straight-edge to draw the line. It will help you identify where the graphs actually cross. Graph the line on the same set of axes. Solve this linear-quadratic system of equations graphically and check your solution:. Whether you graph the "line" first or the "parabola" first is not important.

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