Solving Systems Using Substitution and Elimination

Front

What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables. The solution is the point(s) where the equations intersect.

Front

What does substitution mean in solving systems of equations?

Back

Substitution is a method where one equation is solved for one variable, and that expression is substituted into the other equation.

Front

What does elimination mean in solving systems of equations?

Back

Elimination is a method where equations are added or subtracted to eliminate one variable, making it easier to solve for the other variable.

Front

How do you set up a system of equations from a word problem?

Back

Identify the variables, translate the relationships into equations, and ensure the equations represent the problem accurately.

Front

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

Back

Isolate one variable in one of the equations.

Front

What is the first step in solving a system of equations using elimination?

Back

Align the equations so that like terms are in columns, and then manipulate the equations to eliminate one variable.

Front

If S represents student tickets and A represents adult tickets, what does the equation S + A = 530 represent?

Back

It represents the total number of tickets sold.

Front

In the equation 3S + 4A = 1740, what does each term represent?

Back

3S represents the total revenue from student tickets, and 4A represents the total revenue from adult tickets.

Front

What is the solution to the system of equations 3x + 2y = 16 and 7x + y = 19?

Back

The solution is (2, 5).

Front

What method is best for solving the system 3x + y = -14 and -2x - y = 9?

Back

The best method is elimination.