Solving Systems of Equations (use Desmos)

Front

What is a system of equations?

Back

A set of two or more equations with the same variables that are solved together.

Front

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

Back

It means to plot the equations on a graph and find the point(s) where they intersect, which represents the solution.

Front

What is the elimination method in solving systems of equations?

Back

A method that involves adding or subtracting equations to eliminate one variable, making it easier to solve for the other.

Front

What is the substitution method in solving systems of equations?

Back

A method where one equation is solved for one variable, and that expression is substituted into the other equation.

Front

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

Back

It means the system of equations has a unique solution.

Front

What does it mean if two lines are parallel?

Back

It means the system of equations has no solution, as the lines never intersect.

Front

What does it mean if two lines coincide?

Back

It means the system of equations has infinitely many solutions, as the lines are the same.

Front

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

Back

Substitute the solution back into the original equations to see if both equations are satisfied.

Front

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

Back

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

Front

What is the slope of a line?

Back

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