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 graphical representation of a system of equations?

Back

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

Front

What is the solution to the system of equations y = 3x - 8 and y = 4 - x?

Back

(3, 1)

Front

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

Back

(2, -4)

Front

What is the substitution method in solving systems of equations?

Back

Replacing one variable with an expression from another equation.

Front

What is the elimination method in solving systems of equations?

Back

Adding or subtracting equations to eliminate one variable.

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 equations represent the same line, so every point on the line is a solution.

Front

What is the solution to the system of equations y = 2x + 1 and y = 4x - 1?

Back

(1, 3)