Solve Systems of Equations - Flashcard Review

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 no solution?

Back

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

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

What is the elimination method in solving systems of equations?

Back

A method where equations are added or subtracted to eliminate one variable, making it easier to solve for the other.

Front

How do you determine if a system of equations has infinite solutions?

Back

If the equations represent the same line, they have infinite solutions.

Front

Solve the system of equations by substitution: y = 2x + 3 and 3x + y = 12. What is (x, y)?

Back

(3, 9)

Front

Solve the system of equations by elimination: 2x + 3y = 6 and 4x + 6y = 12. What is (x, y)?

Back

Infinite solutions.

Front

What does it mean for a system of equations to be consistent?

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A system is consistent if it has at least one solution.

Front

What does it mean for a system of equations to be inconsistent?

Back

A system is inconsistent if it has no solutions.

Front

Solve the system of equations: 3x + 4y = 10 and 2x - y = 1. What is (x, y)?

Back

(2, 1)