Systems of Equations

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 point(s) where the equations intersect.

Front

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

Back

A system has one solution when the graphs of the equations intersect at exactly one point.

Front

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

Back

A system has no solution when the graphs of the equations are parallel and never intersect.

Front

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

Back

A system has infinitely many solutions when the equations represent the same line, meaning they intersect at every point on that line.

Front

How do you represent a linear equation in slope-intercept form?

Back

A linear equation in slope-intercept form is represented as y = mx + b, where m is the slope and b is the y-intercept.

Front

What is the slope of the line represented by the equation y = 2x + 3?

Back

The slope of the line is 2.

Front

What is the y-intercept of the line represented by the equation y = -4x + 5?

Back

The y-intercept of the line is 5.

Front

How can you determine if a system of equations is consistent or inconsistent?

Back

A system is consistent if it has at least one solution; it is inconsistent if it has no solutions.

Front

What is the graphical representation of the solution to a system of equations?

Back

The solution is represented by the point(s) where the graphs of the equations intersect.

Front

If two lines intersect at a point, what can you say about their slopes?

Back

If two lines intersect at a point, their slopes are different.