Solving Linear Systems by Graphing

Front

What is a linear system?

Back

A linear system is a set of two or more linear equations with the same variables.

Front

What does it mean to solve a linear system by graphing?

Back

It means to graph the equations on the same coordinate plane and find the point(s) where the lines intersect.

Front

What is the solution to a linear system?

Back

The solution is the point where the graphs of the equations intersect, representing the values of the variables that satisfy all equations.

Front

What does it mean if two lines are parallel in a linear system?

Back

It means they have the same slope and will never intersect, resulting in no solution.

Front

What does it mean if two lines intersect at one point?

Back

It means the system has one unique solution, which is the coordinates of the intersection point.

Front

What does it mean if two lines coincide?

Back

It means they lie on top of each other, resulting in infinitely many solutions.

Front

How do you determine the slope of a line from its equation?

Back

The slope can be determined from the equation in slope-intercept form (y = mx + b), where m is the slope.

Front

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

Back

The slope is 2.

Front

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

Back

The y-intercept is 4.

Front

How can you represent a word problem as a linear equation?

Back

Identify the variables, determine the relationship between them, and express it in equation form.