Linear Systems and Systems of Inequalities

Front

What is a linear system?

Back

A linear system is a collection of one or more linear equations involving the same variables.

Front

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

Back

It means that the lines represented by the equations are parallel and never intersect.

Front

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

Back

It means that the lines represented by the equations intersect at exactly one point.

Front

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

Back

It means that the equations represent the same line, so every point on the line is a solution.

Front

What is the graphical representation of a linear inequality?

Back

It is represented by a shaded region on one side of a boundary line, which can be solid or dotted.

Front

When do you use a solid line when graphing an inequality?

Back

You use a solid line when the inequality includes '≤' or '≥'.

Front

When do you use a dotted line when graphing an inequality?

Back

You use a dotted line when the inequality is '<' or '>'.

Front

How do you determine if a point is a solution to a system of inequalities?

Back

Substitute the point into each inequality; if it satisfies all inequalities, it is a solution.

Front

What is the slope-intercept form of a linear equation?

Back

The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

Front

What is the y-intercept of the equation y = 2x + 10?

Back

The y-intercept is 10.