Solving Systems of linear and quadratic equations

Front

What is a system of equations?

Back

A set of two or more equations with the same variables.

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What does it mean for a system of equations to have no solutions?

Back

It means that the equations represent parallel lines that never intersect.

Front

What is the solution to a system of linear and quadratic equations?

Back

The points where the linear equation intersects the quadratic equation.

Front

How can you determine if a point is a solution to a system of equations?

Back

Substitute the point into each equation; if it satisfies all equations, it is a solution.

Front

What is a linear equation?

Back

An equation that graphs to a straight line, typically in the form y = mx + b.

Front

What is a quadratic equation?

Back

An equation that can be expressed in the form ax² + bx + c = 0, where a ≠ 0.

Front

What is the graphical representation of a linear equation?

Back

A straight line on a coordinate plane.

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What is the graphical representation of a quadratic equation?

Back

A parabola on a coordinate plane.

Front

What does it mean for two equations to be consistent?

Back

It means that the equations have at least one solution.

Front

What does it mean for two equations to be inconsistent?

Back

It means that the equations have no solutions.