Solving 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 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 infinite solutions?

Back

It means that the equations represent the same line, so there are countless points of intersection.

Front

How do you graph a system of equations?

Back

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

Front

What is the substitution method in 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 in solving systems of equations?

Back

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

Front

Solve the system: 2x + 3y = 6 and x - y = 1.

Back

(3, 0) is the solution.

Front

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

Back

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

Front

If two lines intersect at a point, what can be said about the system of equations they represent?

Back

The system has a unique solution.