Graphing 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 two lines are parallel in a system of equations?

Back

It means there is no solution to the system because the lines never intersect.

Front

What does it mean if two lines are the same in a system of equations?

Back

It means there are infinitely many solutions because every point on the line is a solution.

Front

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

Back

The point where the two lines intersect.

Front

How can you determine the number of solutions in a system of equations by graphing?

Back

By observing the relationship between the lines: intersecting (one solution), parallel (no solution), or the same line (infinitely many solutions).

Front

What is the solution to the system of equations y = 2x + 1 and y = -x + 4?

Back

(1, 3)

Front

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

Back

The two lines intersect at exactly one point.

Front

How do you graph a linear equation?

Back

By finding at least two points that satisfy the equation and connecting them with a straight line.

Front

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

Back

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

Front

What is the y-intercept of the equation y = 3x - 5?

Back

-5, which is the point (0, -5) on the graph.