Solving Systems of Equations- all methods

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 are the three main methods for solving systems of equations?

Back

1. Graphing 2. Substitution 3. Elimination

Front

Define 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

Define the elimination method in solving systems of equations.

Back

A method that involves adding or subtracting equations to eliminate one variable, making it easier to solve for the other.

Front

What does it mean if a system of equations has no solution?

Back

It means the lines represented by the equations are parallel and never intersect.

Front

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

Back

It means the equations represent the same line, and there are countless points of intersection.

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

Write the equation for the cost of a pizza with toppings from Palanzio’s Pizzeria.

Back

C = 6.80 + 0.90t, where C is the total cost and t is the number of toppings.

Front

Write the equation for the cost of a pizza with toppings from Guido’s Pizza.

Back

C = 7.30 + 0.65t, where C is the total cost and t is the number of toppings.

Front

Solve the system of equations: y = 4x + 1 and 3x + 2y = 13.

Back

(1, 5)