8.3 Systems of Equations (No Mult)

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 by elimination?

Back

It means to eliminate one variable by adding or subtracting the equations, allowing you to solve for the other variable.

Front

What is the solution to a system of equations?

Back

The point (x, y) where the equations intersect, representing the values of the variables that satisfy all equations in the system.

Front

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

Back

It means the lines represented by the equations are parallel and never intersect.

Front

What does it mean if a system of equations has an infinite number of solutions?

Back

It means the equations represent the same line, so every point on the line is a solution.

Front

Solve by elimination: -2x + 6y = 16 and -8x - 6y = 4

Back

(-2, 2)

Front

Solve by elimination: -4x - 6y = 6 and 4x + 6y = -4

Back

No solution

Front

Solve by elimination: -4x - 4y = 0 and 4x + 4y = 0

Back

Infinite number of solutions

Front

Solve by elimination: 9x - 4y = 7 and -x + 4y = 17

Back

(3, 5)

Front

Solve by elimination: -8x - 10y = 20 and 8x + 6y = 4

Back

(5, -6)