Solving Systems Using Substitution and Elimination

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 substitution method?

Back

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

Front

What is the elimination method?

Back

A method for solving systems of equations by adding or subtracting equations to eliminate one variable.

Front

How do you determine if a point is a solution to a system of equations?

Back

Substitute the point's coordinates into each equation; if both equations are true, the point is a solution.

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 purpose of multiplying an equation in the elimination method?

Back

To create coefficients for one variable that are opposites, allowing for elimination when the equations are added or subtracted.

Front

Solve the system using elimination: 2x + 3y = 6 and 4x - 3y = 12.

Back

(3,0)

Front

Solve the system using substitution: y = 2x + 1 and y = -x + 4.

Back

(1,3)

Front

What is a consistent system of equations?

Back

A system that has at least one solution.