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 a point to be a solution to a system of equations?

Back

It means that the point satisfies all equations in the system.

Front

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

Back

Substitute the x and y values of the point into each equation and check if both equations are true.

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 for two lines to intersect on a graph?

Back

It means they have a common solution, which is the point of intersection.

Front

What is the graphical representation of a system of equations?

Back

It is the graph of each equation plotted on the same coordinate plane.

Front

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

Back

(1, 5) - found by graphing or substitution.

Front

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

Back

They have no solutions because they never intersect.

Front

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

Back

Solve one of the equations for one variable in terms of the other.

Front

What is an ordered pair?

Back

A pair of numbers (x, y) that represent a point on a coordinate plane.