Systems of Equations Flashcard - All Methods

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 for a system of equations to have no solution?

Back

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

Front

What is the graphical representation of a system of equations with infinitely many solutions?

Back

The equations represent the same line, meaning they overlap completely.

Front

How do you solve a system of equations using substitution?

Back

1. Solve one equation for one variable. 2. Substitute that expression into the other equation.

Front

What is the elimination method for solving systems of equations?

Back

A method where you add or subtract equations to eliminate one variable, making it easier to solve for the other.

Front

What is the solution of the system: 5x + y = 10 and 2x - y = 1?

Back

(4, 2)

Front

What is the solution of the graph represented by the equations?

Back

(2, 4)

Front

Solve by elimination: 4x + 9y = 28 and -4x - y = -28. What is the solution?

Back

(7, 0)

Front

Find the solution using substitution: y = 2x + 1 and 3x - y = 4. What is the solution?

Back

(2, 5)

Front

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

Back

A consistent system has at least one solution.