Substitute the values of `a`, `b`, and `c` into the formula.
![solving systems of linear and quadratic equations solving systems of linear and quadratic equations](https://www.onlinemathlearning.com/image-files/linear-quadratic.png)
Now there is a quadratic equation set equal to `0` and we can use the quadratic formula The formula `x=(-b+-sqrt(b^2-4ac))/(2a)` it is used to solve a quadratic equation of the form `ax^2+bx+c=0`., `x=(-b+-sqrt(b^2-4ac))/(2a)`, to find the solution. Subtract `3x` from both sides and subtract `7` from both sides. In this case, both equations have `y` isolated, so we can set them equal. Solve the system using the substitution method `y=x^2-5` and `y=3x+7`. Let's solve a system of a linear and a quadratic equation by graphing: The number of solutions for a system with one linear equation and one quadratic equation is either `0` (never intersect), `1` (intersect in one place), or `2` (intersect in two places). Notice that this means the possible number of solutions for a system of two linear equations is `0` (never intersect), `1` (intersect in one place), or infinity (the lines are identical). It does not make sense to consider the case where the two equations represent the same set of points, since a straight line can never be a parabola, and vice versa. If the line intersects the parabola in two places, then there are two solutions that are true for both equations. If the graphs of the equations do not intersect, then there are no solutions that are true for both equations. If the parabola and the line touch at a single point, then there is one solution that is true for both equations. To solve a system of a linear equation and a quadratic equation, we will do the same thing, find the point-or points-of intersection between the two graphs: If the graphs of the equations are the same, then there are an infinite number of solutions that are true for both equations.
![solving systems of linear and quadratic equations solving systems of linear and quadratic equations](https://i.pinimg.com/originals/fe/54/a6/fe54a69846a9e9ba926a519f9e1a805d.jpg)
If the graphs of the equations do not intersect (for example, if they are parallel), then there are no solutions that are true for both equations. If the graphs of the equations intersect, then there is one solution that is true for both equations. There may be one solution, no solution, or an infinite number of solutions to a system of two linear equations: The solution to this kind of system is the point of intersection between the two lines, or the place where the two equations have the same `x` and `y` values. Let’s begin by talking about two linear equations. Systems of Linear and Quadratic Equations