System 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 graphical representation of a system of equations?

Back

The point(s) where the graphs of the equations intersect.

Front

What is an ordered pair?

Back

A pair of numbers (x, y) that represent a point on a coordinate plane.

Front

What is the solution to the system of equations y = 2x + 3 and y = -x + 1?

Back

(1, 5)

Front

How can you determine if a system of equations has no solution?

Back

If 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.

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

What is the solution to the system of equations 3x + 2y = 6 and x - y = 1?

Back

(2, 0)