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

What happens when two lines intersect at one point?

Back

The system has one unique solution.

Front

What does it mean if two lines are parallel?

Back

They have the same slope but different y-intercepts, resulting in no solutions.

Front

What does it mean if two lines are the same?

Back

They have infinite solutions because every point on the line is a solution.

Front

How do you determine if a system of equations has no solution?

Back

If the lines are parallel, they will never intersect.

Front

How do you determine if a system of equations has infinite solutions?

Back

If the equations represent the same line, they will intersect at every point on the line.

Front

What is substitution in solving systems of equations?

Back

It involves solving one equation for one variable and substituting that expression into the other equation.

Front

What is the graphical representation of the equation y = mx + b?

Back

It is a straight line where m is the slope and b is the y-intercept.