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 a system of equations has one solution?

Back

The lines intersect at exactly one point.

Front

What does it mean if a system of equations has 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 coincide, meaning they are the same line.

Front

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

Back

By identifying the intersection point of the lines 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.

Front

If y = 2x + 3, what is y when x = 1?

Back

y = 5.

Front

What is the solution to the system of equations: y = 3x + 1 and y = -x + 4?

Back

(1, 4).