Linear Equations

Question 1

What is a linear equation?

Answer 1

A linear equation is just
two expressions separated by an equals sign. A linear equation (as opposed to some other sort of equation, such as a quadratic
equation) is an equation in which the variables aren’t modified by exponents or roots.

Question 2

What is a fundamental concept of linear equations?

Answer 2

The fundamental concept behind solving linear equations (in fact, any kind of equation) is this: you can do anything you want to manipulate one side of the equation, so long as you do it to both sides.

Question 3

Solve for z in terms of x and y:

x + y = x(y + z)

Answer 3

x + y = x(y + z)
x + y = xy + xz (multiply out the parentheses)
x+y-xy/x =xz/x (divide both sides by x)
z =x+y-xy/x (complete the division)

Simplify further if necessary

x+y-xy/x =x/x +y/x-xy/x = 1 + y/x-y

Question 4

What is the general rule for solving systems of equations?

Answer 4

If you have n variables, you need n linear equations to solve for
those variables (a “system” of n equations)