Systems of Equations

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 one solution?

Back

The lines representing the equations intersect at exactly one point.

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 does it mean if a system of equations has infinitely many solutions?

Back

The lines representing the equations coincide, meaning they are the same line.

Front

How do you solve a system of equations by substitution?

Back

Solve one equation for one variable and substitute that expression into the other equation.

Front

How do you solve a system of equations by elimination?

Back

Add or subtract the equations to eliminate one variable, making it easier to solve for the other.

Front

What is the graphical representation of a system of equations?

Back

The graphical representation consists of lines or curves on a coordinate plane.

Front

What is the solution to the system of equations 3x + 2y = 16 and 7x + y = 19?

Back

(2, 5)

Front

What is the solution to the system of equations -x + y = -13 and -8x - 4y = -8?

Back

(5, -8)

Front

What is the solution to the system of equations 2x + 4y = 450 and 3x + 2y = 315?

Back

(x, y) where x and y are the values that satisfy both equations.