Jan 12 Solving Systems of Equations by Substitution

Front

What is a system of equations?

Back

A set of two or more equations with the same variables that are solved together.

Front

What does it mean for a system of equations to have infinite solutions?

Back

It means that the equations represent the same line, and every point on that line is a solution.

Front

What does it mean for a system of equations to have no solution?

Back

It means that the equations represent parallel lines that never 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

How do you determine if a system of equations has one solution?

Back

If the lines represented by the equations intersect at exactly one point.

Front

What is the graphical representation of a system of equations with infinite solutions?

Back

Two overlapping lines on a graph.

Front

What is the graphical representation of a system of equations with no solution?

Back

Two parallel lines on a graph.

Front

What is an example of a statement that results in no solution?

Back

4 = 7, which is a false statement.

Front

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

Back

(1, 5)

Front

Solve the system of equations: 2x + 3y = 6 and 4x + 6y = 12. What is the solution?

Back

Infinite solutions.