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 two lines to intersect on a graph?

Back

It means that the two equations have a common solution, represented by the point of intersection.

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

How do you determine if a system of equations has no solution?

Back

If the lines represented by the equations are parallel, they will never intersect, indicating no solution.

Front

What is the graphical representation of a solution to a system of equations?

Back

The point where the graphs of the equations intersect.

Front

What does it mean if a system of equations has infinitely many solutions?

Back

The equations represent the same line, meaning every point on the line is a solution.

Front

How can you check your solution to a system of equations?

Back

By substituting the solution back into both original equations to see if they hold true.

Front

What is the first step in using substitution to solve a system of equations?

Back

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

Front

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

Back

(−2, −1)

Front

What does the term 'no solution' indicate in the context of systems of equations?

Back

It indicates that the equations represent parallel lines that do not intersect.