Solving Systems of Equations and Inequalities

Front

What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables. The solution is the set of values that satisfy all equations simultaneously.

Front

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

Back

A system has no solutions when the equations represent parallel lines that never intersect.

Front

What is the graphical representation of a linear equation?

Back

A linear equation is represented graphically as a straight line in a coordinate plane.

Front

What is the quadratic formula?

Back

Front

How do you determine the number of solutions in a linear-quadratic system?

Back

The number of solutions can be determined by analyzing the intersection points of the linear and quadratic graphs. They can intersect at 0, 1, or 2 points.

Front

What is the vertex of a parabola?

Back

The vertex of a parabola is the highest or lowest point on the graph, depending on whether it opens upwards or downwards.

Front

What is the discriminant in a quadratic equation?

Back

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions, indicating that one is greater than, less than, or not equal to the other.

Front

How do you solve a quadratic inequality?

Back

To solve a quadratic inequality, first find the roots of the corresponding quadratic equation, then test intervals to determine where the inequality holds true.

Front

What is the significance of the y-intercept in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, representing the value of y when x = 0.