Solving Systems by Graphing and Substitution

Front

What is a system of equations?

Back

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

Front

What does it mean for two lines to intersect?

Back

It means they have exactly one solution, which is the point where they cross.

Front

What is the graphical representation of a system with no solution?

Back

The lines are parallel and never intersect.

Front

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

Back

The lines overlap each other, meaning they are the same line.

Front

How do you solve a system of equations by graphing?

Back

Graph each equation on the same coordinate plane and identify the point of intersection.

Front

What is substitution in solving systems of equations?

Back

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

Front

What is the solution to the system y = 2x + 3 and y = -x + 1?

Back

(−2, −1) is the solution.

Front

What does it mean if two lines are coincident?

Back

They lie on top of each other and have infinitely many solutions.

Front

What is the slope-intercept form of a line?

Back

It is written as y = mx + b, where m is the slope and b is the y-intercept.

Front

How can you determine if a system has one solution, no solution, or infinitely many solutions?

Back

By analyzing the slopes and y-intercepts of the lines.