Solving Systems of Equations

Front

What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables. The solution is the point(s) where the equations intersect.

Front

What does it mean to solve a system of equations by elimination?

Back

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

Front

What is the elimination method?

Back

The elimination method is a technique for solving systems of equations by removing one variable, allowing for the solution of the remaining variable.

Front

How do you eliminate a variable in a system of equations?

Back

To eliminate a variable, you can multiply one or both equations by a number so that when added or subtracted, one variable cancels out.

Front

What is the first step in solving the system 2x + 3y = 12 and 5x - y = 13 by elimination?

Back

The first step is to manipulate the equations so that when added or subtracted, one variable will be eliminated.

Front

Solve the system by elimination: 2x + 3y = 12 and 5x - y = 13.

Back

(3, 2)

Front

What is the solution to the system 4x + 9y = 28 and -4x - y = -28?

Back

(7, 0)

Front

What does it mean if a system of equations has no solution?

Back

A system has no solution if the equations represent parallel lines that never intersect.

Front

What is the solution to the system 2x + 10y = -20 and -x + 4y = 28?

Back

(-20, 2)

Front

What is the solution to the system -9x - 4y = -20 and 5x + 4y = 4?

Back

(4, -4)