Solving Linear Systems by Graphing

Front

What is a linear system?

Back

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

Front

What does it mean if a linear system has no solution?

Back

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

Front

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

Back

It means that the lines representing the equations coincide, or are the same line.

Front

How do you graph a linear equation?

Back

To graph a linear equation, you can find two or more points that satisfy the equation and plot them on a coordinate plane.

Front

What is the solution to a system of equations?

Back

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

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

How can you determine if a system of equations has one solution?

Back

If the lines intersect at exactly one point, the system has one solution.

Front

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

Back

The y-intercept is the point where the line crosses the y-axis, indicating the value of y when x = 0.

Front

What does it mean for two lines to be perpendicular?

Back

Two lines are perpendicular if the product of their slopes is -1.

Front

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

Back

You find the intersection point by plotting both lines on the same graph and identifying where they cross.