# Systems of linear and quadratic equations

## Systems of Linear and Quadratic Equations 9-8 Systems of Linear and Quadratic Equations

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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.

By using our site, you acknowledge that you have read and understand our Cookie Policy , Privacy Policy , and our Terms of Service. MathOverflow is a question and answer site for professional mathematicians. It only takes a minute to sign up. Suppose we have a system of linear and quadratic equations with rational coefficients and we want to find out whether this system has a real solution or not. The actual values of a solution is not important. So my Question is this: is there a polynomial time algorithm to determine the existence of a real solution? Note that the existence of a complex solution can be checked by computing a groebner basis for the relevant ideal and checking that this ideal is not the entire polynomial ring by weak Nullstellensatz.

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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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. This example will graph the parabola first.

## Use graphing to solve quadratic equations

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.

## Systems of linear & quadratic equations

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