Systems of Linear Equations

Front

What is a system of linear equations?

Back

A set of two or more linear equations with the same variables.

Front

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

Back

The lines representing the equations are parallel and never intersect.

Front

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

Back

The lines representing the equations are the same line, overlapping each 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

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

Solve for x and y: y = x - 3, y = -x + 3

Back

(3, 0)

Front

Solve for x and y: 5x + 2y = 12, -5x + 4y = -66

Back

(6, -9)

Front

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

Back

(2, 5)

Front

What does the graph of intersecting lines represent in a system of equations?

Back

It represents a unique solution where the two equations intersect at one point.

Front

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

Back

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