Solving Systems Algebraically

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 algebraically?

Back

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

Front

What is the elimination method?

Back

A technique for solving systems of equations by adding or subtracting equations to eliminate one 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

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

Back

The lines represented by the equations are parallel and never intersect.

Front

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

Back

The equations represent the same line, meaning every point on the line is a solution.

Front

How do you determine if two equations are equivalent?

Back

If one equation can be transformed into the other by algebraic manipulation, they are equivalent.

Front

What is the first step in solving the system: 3x + 2y = 8 and -3x + 6y = 12?

Back

Add the equations to eliminate x.

Front

What is the solution to the system: 4x + 4y = 4 and 3x + 4y = 10?

Back

(-6, 7) is the solution.

Front

What is the first step in solving the system: 3x + 3y = 3 and y = 3x + 5?

Back

Substitute y from the second equation into the first equation.