Semester 1 Final exam Math 3

Front

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

Back

It means that the equations represent the same line, resulting in every point on the line being a solution.

Front

What is the first step in finding the inverse of a function?

Back

Replace f(x) with y.

Front

What is the second step in finding the inverse of a function?

Back

Switch the x's and y's.

Front

What is the final step in finding the inverse of a function after switching x and y?

Back

Solve for y.

Front

Back

Front

How do you solve the system of equations: y = 4x + 1 and 3x + 2y = 13?

Back

Substitute y in the second equation to find x, then use x to find y. The solution is (1, 5).

Front

Back

Front

What is a system of equations?

Back

A set of two or more equations with the same variables.

Front

What does it mean for two equations to be independent?

Back

They have exactly one solution, meaning they intersect at one point.

Front

What does it mean for two equations to be dependent?

Back

They have infinitely many solutions, meaning they represent the same line.