22 - 23 Flashcard - Substitution / Elimination

Front

What is a system of equations?

Back

A set of two or more equations with the same variables that are solved together.

Front

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

Back

It means that the equations represent the same line, and every point on that line is a solution.

Front

What is the elimination method in solving systems of equations?

Back

A method that involves adding or subtracting equations to eliminate one variable, making it easier to solve for the other.

Front

What is the substitution method in solving systems of equations?

Back

A method where one equation is solved for one variable, and that expression is substituted into the other equation.

Front

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

Back

By substituting the point's coordinates into both equations and checking if both equations are satisfied.

Front

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

Back

It means that the equations represent parallel lines that never intersect.

Front

Solve the system using elimination: 4x + 8y = 20 and -4x + 2y = -30.

Back

(7, -1)

Front

Solve the system using substitution: y = 2x + 6 and y = -x - 3.

Back

(-3, 0)

Front

What is the first step in solving a system of equations using elimination?

Back

Align the equations so that like terms are in the same column.

Front

What is the first step in solving a system of equations using substitution?

Back

Solve one of the equations for one variable in terms of the other.