Systems of equations and inequalities

Front

What is a system of equations?

Back

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

Front

What does it mean for a system of equations to have a solution?

Back

A solution is a set of values for the variables that makes all equations true.

Front

What is an infinite solution in a system of equations?

Back

When there are countless solutions that satisfy all equations, often when the equations represent the same line.

Front

What does it mean if a system of equations has no solution?

Back

The equations represent parallel lines that never intersect.

Front

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

Back

Substitute the point's coordinates into each equation; if all equations are satisfied, it is a solution.

Front

What is the graphical representation of a system of inequalities?

Back

The solution set is represented by the overlapping shaded regions of the inequalities.

Front

What is the significance of the intersection point in a system of equations?

Back

The intersection point represents the solution to the system, where both equations are satisfied.

Front

How do you solve a system of equations using substitution?

Back

Solve one equation for one variable, then substitute that expression into the other equation.

Front

What is the elimination method in solving systems of equations?

Back

Adding or subtracting equations to eliminate one variable, making it easier to solve for the other.

Front

What does it mean for two lines to be parallel in the context of systems of equations?

Back

They have the same slope but different y-intercepts, resulting in no solutions.