Algebra 1 5.3-5.4 Flashcard

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 involves adding or subtracting the equations to eliminate one variable, making it easier 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

The lines represented by the equations are parallel and never intersect.

Front

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

Back

The equations represent the same line, meaning every point on the line is a solution.

Front

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

Back

By analyzing the slopes and intercepts of the lines represented by the equations.

Front

Solve the system of equations: 7x + 4y = -6 and -7x - 6y = 30.

Back

(6, -12)

Front

Solve by elimination: -12x - 4y = -8 and -6x - 2y = -4.

Back

infinite solutions

Front

Solve the system of equations: 3x + y = -14 and -2x - y = 9.

Back

(-5, 1)

Front

Solve by elimination: 2x + 9y = -7 and 6x - 3y = 9.

Back

(1, -1)