# Math 20-1 Question ?

It is possible for systems of linear-quadratic and quadratic-quadratic equations to have no solutions.

a. Give an example of each type of system where there are no solutions.

b. For each case, show how solving the system algebraically would lead to the conclusion that there are no solutions.

### 2 Answers

- Jeffrey KLv 61 month ago
Draw a U shaped parabola on a graph then draw a straight line that does not cross the parabola.

Draw two parabolas on a graph that do not cross each other.

If you try to solve a system of equations that had no solution algebraically, both the x and y variables will disappear, leaving an equation with different numbers on each side of equal sign.

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- PopeLv 71 month ago
For most of us, a quadratic equation is a second-degree equation in one variable. In this context, together with your recent activity, I think it is likely that you are interpreting a quadratic equation as a second-degree equation in two variables. You may even mean specifically y equated with a quadratic function of x.

Yes, that is possible in both cases. Consider their graphs. The graph of a linear equation is a line. The graph of a second-degree equation is a conic section. Use a parabola for simplicity. It is possible to define a line and a parabola that do not intersect. It also is possible to define two parabolas that do not intersect.

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