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 elimination method?

Back

A technique for solving systems of equations by removing one variable, allowing for easier solving.

Front

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

Back

The lines represented by 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, meaning every point on the line is a solution.

Front

How do you determine if a system of equations has one solution?

Back

The lines intersect at exactly one point.

Front

Solve by elimination: 3x + 7y = 23 and -3x - 7y = -17

Back

No solution.

Front

Solve for x and y: 3x + 2y = 16 and 7x + y = 19

Back

(2, 5).

Front

Solve by elimination: 4x + 9y = 28 and -4x - y = -28

Back

(7, 0).

Front

Solve for x and y: 2x - 3y = -1 and y = x - 1

Back

(4, 3).