Solving Systems with elimination 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 to solve a system of equations?

Back

Finding the values of the variables that satisfy all equations in the system.

Front

What is the elimination method?

Back

A technique for solving systems of equations by adding or subtracting equations to eliminate a variable.

Front

What is the substitution method?

Back

A technique for solving systems of equations by solving one equation for one variable and substituting that expression into the other equation.

Front

How do you eliminate a variable in a system of equations?

Back

Adjust the equations so that when added or subtracted, one variable cancels out.

Front

What is the first step in the elimination method?

Back

Align the equations so that corresponding variables and constants are in the same columns.

Front

What is the first step in the substitution method?

Back

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

Front

If you have the equations 5x + 2y = 23 and 3x - 4y = -7, what is the solution using elimination?

Back

(3, 4) - found by eliminating y.

Front

If you have the equations -5x + 2y = -1 and 5x - 3y = -1, what is the solution using elimination?

Back

(1, 2) - found by eliminating x.

Front

If x = 1 and y = 4x - 1, what is the solution using substitution?

Back

(1, 3) - substitute x into the second equation.