solve systems by graphing

Front

What is a system of equations?

Back

A set of two or more equations with the same variables.

Front

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

Back

It means to find the point(s) where the graphs of the equations intersect.

Front

What is the solution to a system of equations?

Back

The point(s) where the equations intersect, representing the values of the variables that satisfy all equations.

Front

How do you graph a linear equation?

Back

You can graph a linear equation by finding two or more points that satisfy the equation and connecting them with a straight line.

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

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 equation y = -x + 5?

Back

The y-intercept is 5.

Front

How can you determine if a point is a solution to a system of equations?

Back

Substitute the point's coordinates into each equation; if it satisfies all equations, it is a solution.

Front

What does it mean if two lines are parallel when graphing a system of equations?

Back

It means the system has no solution because the lines never intersect.

Front

What does it mean if two lines are coincident when graphing a system of equations?

Back

It means the system has infinitely many solutions because the lines overlap.