System of Equations by Graphing

Front

What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables. The solution is the point(s) where the equations intersect.

Front

What does it mean to solve a system of equations by graphing?

Back

To solve a system of equations by graphing means to plot the equations on a graph and identify the point(s) where they intersect, which represents the solution.

Front

What is the solution to a system of equations?

Back

The solution to a system of equations is the set of values for the variables that make all equations true, often represented as an ordered pair (x, y).

Front

How do you graph the equation y = mx + b?

Back

To graph y = mx + b, identify the y-intercept (b) on the y-axis, then use the slope (m) to find another point by rising and running from the y-intercept.

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, calculated as the change in y divided by the change in x (rise/run).

Front

What is the y-intercept of a line?

Back

The y-intercept is the point where the line crosses the y-axis, represented as (0, b) in the equation y = mx + b.

Front

What does it mean if two lines are parallel?

Back

If two lines are parallel, they have the same slope and will never intersect, meaning there is no solution to the system of equations.

Front

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

Back

If two lines intersect at one point, it means there is exactly one solution to the system of equations, represented by the coordinates of the intersection point.

Front

What does it mean if two lines are coincident?

Back

If two lines are coincident, they lie on top of each other and have infinitely many solutions, as every point on the line is a solution.

Front

How can you check the solution of a system of equations?

Back

You can check the solution by substituting the values of the solution back into the original equations to see if they hold true.