Solving Systems of Equations

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 graphical representation of a system of equations?

Back

The intersection points of the lines representing the equations.

Front

What are the possible outcomes when solving a system of equations?

Back

No solution, one solution, or infinitely many solutions.

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 a variable and substituting that expression into the other equation.

Front

How do you determine if a system has no solution?

Back

If the equations represent parallel lines that never intersect.

Front

How do you determine if a system has infinitely many solutions?

Back

If the equations represent the same line, meaning they are dependent.

Front

Solve by elimination: 2x + 3y = 6 and 4x - 3y = 12.

Back

(3, 0)

Front

Solve by substitution: y = 2x + 1 and 3x - y = 4.

Back

(1, 3)