Systems of linear equations

Front

What is a system of linear equations?

Back

A set of two or more linear equations in the same variables.

Front

How can you tell if a point is a solution to a system of linear equations?

Back

The (x,y) coordinates satisfy both equations.

Front

Solve the system of equations by substitution: y = -4x + 5 and y = 3x - 16.

Back

(3, -7)

Front

Solve for x and y: 3x + 2y = 16 and 7x + y = 19.

Back

(2, 5)

Front

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

Back

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

Front

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

Back

The equations represent parallel lines that never intersect.

Front

Solve the system using any method: -4x - 4y = 0 and 4x + 4y = 0.

Back

Infinite number of solutions.

Front

What is the graphical representation of a system of linear equations?

Back

The intersection points of the lines represent the solutions to the system.

Front

What is substitution in the context of solving systems of equations?

Back

Replacing one variable with an expression derived from another equation.

Front

What is elimination in the context of solving systems of equations?

Back

Adding or subtracting equations to eliminate one variable.