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.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

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.

Tags

CCSS.8.EE.C.8A

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

Tags

CCSS.HSA-REI.B.4B

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.

Tags

CCSS.HSA.REI.C.7

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

Tags

CCSS.HSA-REI.B.4B

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.

Tags

CCSS.6.EE.B.8

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.