Systems of Equations -- Elimination

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 to solve a system of equations using elimination?

Back

It 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

A technique used to solve systems of equations by eliminating one variable through addition or subtraction.

Front

How do you determine if a system of equations has one solution, no solution, or infinitely many solutions?

Back

If the lines intersect at one point, there is one solution; if they are parallel, there is no solution; if they are the same line, there are infinitely many solutions.

Front

What is the first step in solving a system of equations by elimination?

Back

Align the equations and manipulate them to have the same coefficient for one of the variables.

Front

Solve the system using elimination: 3x + 2y = 16 and 7x + y = 19.

Back

(2, 5)

Front

Solve for x and y: 3x - 3y = 33 and 6x - 3y = 57.

Back

(8, -3)

Front

Where do these lines intersect: x - y = 11 and 2x + y = 19?

Back

(10, -1)

Front

Solve the system by elimination: -8x - 10y = 20 and -8x - 6y = -4.

Back

(5, -6)

Front

Solve by elimination: 4x + 9y = 28 and -4x - y = -28.

Back

(7, 0)