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 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 values of the variables that make all equations in the system true.

Front

What is substitution 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 is slope-intercept form?

Back

A way of writing linear equations in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

How do you find the y-intercept of a line?

Back

Set x = 0 in the equation of the line and solve for y.

Front

What is the first step in solving a system by substitution?

Back

Look for an equation that is solved for a variable (x= or y=).

Front

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

Back

It means there is no solution to the system because the lines never intersect.

Front

What is the graphical representation of the solution (1, -4)?

Back

It is the point where the x-coordinate is 1 and the y-coordinate is -4 on the graph.

Front

How do you check if a solution is correct for a system of equations?

Back

Substitute the solution back into both equations to see if they hold true.