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 substitution method?

Back

A method for solving a system of equations by solving one equation for one variable and substituting that expression into the other equation.

Front

What is the elimination method?

Back

A method for solving a system of equations by adding or subtracting equations to eliminate one variable.

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 represented by the equations intersect at exactly one point.

Front

What is the first step in solving using the substitution method?

Back

Get either variable by itself.

Front

Given the equations y = 2x + 3 and y = -x + 1, how do you find the solution?

Back

Set the equations equal to each other: 2x + 3 = -x + 1, then solve for x.

Front

What is the graphical representation of a system of equations?

Back

The intersection points of the lines representing the equations.