Systems of Linear Equations

Front

What is a system of linear equations?

Back

A set of two or more linear equations with the same variables.

Front

What does it mean for a system of equations to have a unique solution?

Back

It means there is exactly one set of values for the variables that satisfies all equations in the system.

Front

What does it mean for a system of equations to have no solution?

Back

It means that the equations represent parallel lines that never intersect.

Front

What does it mean for a system of equations to have infinitely many solutions?

Back

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

Front

How do you solve a system of linear equations by graphing?

Back

You graph each equation on the same coordinate plane and identify the point(s) where the lines intersect.

Front

What is the substitution method for solving systems of equations?

Back

It involves 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

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

Front

What is the graphical representation of the solution to a system of equations?

Back

The solution is represented by the point(s) where the graphs of the equations intersect.

Front

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

Back

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

Front

How can you determine if two lines are parallel?

Back

Two lines are parallel if they have the same slope but different y-intercepts.