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 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 are parallel when graphing a system of equations?

Back

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

Front

What does it mean if two lines coincide when graphing a system of equations?

Back

It means there are infinitely many solutions, as the lines overlap completely.

Front

How do you determine the solution of a system of equations graphically?

Back

By identifying the point(s) where the lines intersect on the graph.

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

If a system of equations has one solution, what does that indicate about the lines?

Back

The lines intersect at exactly one point.

Front

What is the solution to the system of equations y = 2x + 1 and y = -x + 4?

Back

(1, 3) - The point where the two lines intersect.

Front

What is the graphical representation of the equation y = 3x - 5?

Back

A straight line with a slope of 3 and a y-intercept of -5.