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Recall that the discriminant of a quadratic equation 𝑎 𝑥 + 𝑏 𝑥 + 𝑐 = 0  is the expression 𝑏 − 4 𝑎 𝑐  . If the discriminant is negative, then we know that the quadratic equation will have complex roots.

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A line can either touch or intersect a parabola, circle or ellipse. Hence a system of a quadratic and a linear equation has no, 1 or 2 solutions.

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1. Solve the resulting quadratic equation to find the x-value(s) of the solution(s).

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A System of those two equations can be solved (find where they intersect), either:

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when there is no intersection points.

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Recall that the discriminant of a quadratic equation 𝑎 𝑥 + 𝑏 𝑥 + 𝑐 = 0  is the expression 𝑏 − 4 𝑎 𝑐  . If the discriminant is negative, then we know that the quadratic equation will have complex roots.

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Most linear systems you will encounter will have exactly one solution. However, it is possible that there are no solutions, or infinitely many. (It is not possible that there are exactly two solutions.)

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A line can either touch or intersect a parabola, circle or ellipse. Hence a system of a quadratic and a linear equation has no, 1 or 2 solutions.

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Isolate one of the two variables in one of the equations. Substitute the expression that is equal to the isolated variable from Step 1 into the other equation.Solve the resulting quadratic equation to find the x-value(s) of the solution(s).

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A System of those two equations can be solved (find where they intersect), either:

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1. Solve the resulting quadratic equation to find the x-value(s) of the solution(s).

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Rewrite both equations in slope-intercept form. Compare the m- and b-values of the equations to determine the number of solutions.