Identifying Solutions to Systems of Equations

Front

What is a system of equations?

Back

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

Front

What does it mean if a system of equations has one solution?

Back

The lines representing the equations intersect at exactly one point.

Front

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

Back

The lines representing the equations are parallel and never intersect.

Front

What does it mean if a system of equations has infinitely many solutions?

Back

The lines representing the equations are the same line, overlapping completely.

Front

How can you determine if two equations have the same slope?

Back

If the coefficients of x in both equations are equal when in slope-intercept form (y = mx + b).

Front

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

Back

The slope is 2.

Front

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

Back

The slope is 3/2.

Front

If two lines have slopes of 5/2, what can be said about their relationship?

Back

If they have different y-intercepts, they are parallel and have no solutions.

Front

What is the graphical representation of the equation y = (1/4)x - 2?

Back

A line with a slope of 1/4 that crosses the y-axis at -2.

Front

What is the graphical representation of the equation y = 3x + 9?

Back

A line with a slope of 3 that crosses the y-axis at 9.