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 graphs of the equations represent the solutions.

Front

What is substitution in solving systems of equations?

Back

Replacing one variable with an expression derived from another equation.

Front

What is elimination in solving systems of equations?

Back

A method that involves adding or subtracting equations to eliminate a variable.

Front

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

Back

The lines representing the equations are parallel and never intersect.

Front

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

Back

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

Front

How do you determine the number of solutions in a system of equations?

Back

By analyzing the slopes and intercepts of the equations when graphed.

Front

What is the solution to the system: x = 6 and y = 2x - 3?

Back

(6, 9)

Front

What is the solution to the system: 3x + 7y = 23 and -3x - 7y = -17?

Back

No solution.