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 for a point to be a solution to a system of equations?

Back

The (x,y) coordinates satisfy both equations in the system.

Front

How can you solve a system of equations?

Back

By using methods such as substitution, elimination, or graphing.

Front

What is substitution in solving systems of equations?

Back

Replacing one variable with an expression from another equation.

Front

What is elimination in solving systems of equations?

Back

Adding or subtracting equations to eliminate one variable.

Front

What does it mean if two equations are inconsistent?

Back

They have no solution; the lines are parallel.

Front

What does it mean if two equations are dependent?

Back

They have infinitely many solutions; the lines are the same.

Front

What is the graphical representation of a system of equations?

Back

The point(s) where the lines intersect represent the solution(s).

Front

How do you check if a solution is correct?

Back

Substitute the solution back into both equations to see if they hold true.

Front

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

Back

(0, 2) is the solution.