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 no solution?

Back

It means that the lines represented by the equations are parallel and 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 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 find the point(s) where they intersect.

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

Back

(0,0)

Front

What is the solution to the system: -4x - 2y = -12 and 4x + 8y = -24?

Back

(6,-6)

Front

What is the solution to the system: 4x + 8y = 20 and -4x + 2y = -30?

Back

(7,-1)

Front

What is the solution to the system: Solve by graphing: y = 2x + 4 and y = -x + 2?

Back

(4,2)