Solving 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.

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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 there are no values for the variables that can satisfy all equations in the system, often because the lines are parallel.

Front

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

Back

It means there are countless sets of values for the variables that satisfy all equations, often because the equations represent the same line.

Front

How do you graph a system of equations?

Back

You graph each equation on the same coordinate plane and look for points of intersection.

Front

What is the substitution method for solving systems of equations?

Back

A method where you solve one equation for one variable and substitute that expression into the other equation.

Front

What is the elimination method for solving systems of equations?

Back

A method where you add or subtract equations to eliminate one variable, making it easier to solve for the other.

Front

What is the point of intersection in a graph of two lines?

Back

The point where the two lines cross, representing the solution to the system of equations.

Front

How do you determine if two lines are parallel?

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If they have the same slope but different y-intercepts, they will never intersect and thus have no solution.

Front

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

Back

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