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.

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 there are no values for the variables that can satisfy all equations in the system.

Front

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

Back

It means that there are an unlimited number of values for the variables that satisfy all equations in the system.

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 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

What is the y-coordinate of the solution to the system: x - 2y = 1 and x + 4y = 7?

Back

1

Front

What is the solution to the system: 2x - y = 0 and 4x - y = 0?

Back

(0, 0) - Infinite solutions.

Front

Solve for x and y: y = 2/3x - 2 and y = -x + 3.

Back

(3, 0) - The point where the two lines intersect.