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 a solution to a system of equations?

Back

A set of values for the variables that makes all equations true.

Front

What is the graphical representation of a system of equations?

Back

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

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

How do you determine if a system of equations has one solution, no solution, or infinitely many solutions?

Back

By analyzing the slopes and y-intercepts of the lines represented by the equations.

Front

What is the substitution method for solving systems of equations?

Back

Solving one equation for one variable and substituting that expression into the other equation.

Front

What is the elimination method for solving systems of equations?

Back

Adding or subtracting equations to eliminate one variable, making it easier to solve for the other.

Front

What is the slope-intercept form of a linear equation?

Back

y = mx + b, where m is the slope and b is the y-intercept.