Solving System of Equations

Front

What does the graph of a system of equations with infinitely many solutions look like?

Back

The same line (coinciding lines)

Front

Write the system of equations for the cost of a large pizza at Palanzio’s Pizzeria ($6.80 + $0.90 per topping) and Guido’s Pizza ($7.30 + $0.65 per topping).

Back

y = 6.80 + 0.90x and y = 7.30 + 0.65x

Front

Solve this system by substitution: 2x + 3y = 12, y = 2x - 1.

Back

(3, 2)

Front

Solve for x and y: 5x + 3y = 7, y = 4.

Back

(-1, 4)

Front

Caitlin has 49 bills totaling $1,430. Write a system where T = # of $20 bills and F = # of $50 bills.

Back

T + F = 49 and 20T + 50F = 1430

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 be parallel in a system of equations?

Back

They have no solutions because they 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

What is the elimination method in solving systems of equations?

Back

A method where equations are added or subtracted to eliminate one variable.

Front

What does it mean for a system of equations to be inconsistent?

Back

It has no solutions, typically represented by parallel lines.