Solving Systems of Equations by Graphing

Front

What is a system of linear equations?

Back

A set of 2 or more equations that have the same variables.

Front

What does it mean for two lines to be coincident?

Back

Coincident lines are lines that lie on top of each other, having infinitely many solutions.

Front

What is the graphical representation of a system of equations with no solution?

Back

Two parallel lines that never intersect.

Front

What is the graphical representation of a system of equations with exactly one solution?

Back

Two lines that intersect at a single point.

Front

How can you determine if two equations represent the same line?

Back

If one equation can be transformed into the other by multiplying or dividing by a non-zero constant.

Front

What is the solution to a system of equations?

Back

The point(s) where the graphs of the equations intersect.

Front

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

Back

The equations represent the same line, so every point on the line is a solution.

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

How do you find the intersection point of two lines graphically?

Back

Plot both lines on the same graph and identify the point where they cross.

Front

What is the significance of the y-intercept in a linear equation?

Back

It is the point where the line crosses the y-axis (x=0).