Equations

Question 0

Define equivalent equations.

Answer 0

Those equations that have the same solution.

Example:

2+x=3

And

4+2x=6

Question 1

What are the solutions of an equation?

Answer 1

Those values that satisfy the equation, when they are substituted for the unknowns of the equation.

An equation may have no solution or one pr more solutions. If two or more equations are to be solved together, the solutions must satisfy all of the equatiins simultaneously.

Question 2

How do you solve a linear equation with one unknown?

Answer 2

The unknown should be isolated on one side of the equation. This can be done by performing the same mathematical operations on both sides of the equation.

Question 3

How do you solve two linear equations with two unknowns?

Answer 3

One way to solve for two unknowns is to express one of the unknowns in terms of the other.

Example:

(1) 3x+2y=11
(2) x-y=2

Isolate x on the second equation, which will give you x=2+y and substitute this for x in equation 1.

3(2+y)+y=11
6+3y+2y=11
6+5y=11
5y=5
Y=1

If y =1, then x=2+1=3

Question 4

What are the steps to solve equations by factoring?

Answer 4

1. Add or subtract expressions to bring all the expressions to one side of the equation with 0 on the other side.
2. Try to factor the non-zero side into a product of expressions.

Th solutions of the simpler equations will be solutions of the factored equation. These are also called the roots of the equation.

Question 5

How do you use the quadratic formula?

Answer 5

If ax^2+bx+c=0 (a not = 0), then the roots are x=-b+|b^2-4ac|/2a and x=-b-|b^2-4ac|/2a.