This document discusses different types of algebraic equations and methods for solving them. It defines variables and constants, and explains that the goal is to find variable values that satisfy the equations. Linear equations are of the form ax+b=0 and can be solved by subtracting b from both sides and dividing both sides by a. Quadratic equations contain x^2 and can be solved using factorization, completing the square, the quadratic formula, or graphing. Simultaneous equations involve two or more equations with two or more variables, which can be solved using elimination to progressively reduce the number of variables until a solution is obtained.

1. ALGEBRAIC EQUATIONS

2. ALGEBRAIC EQUATIONS
• Quantities like a, b, c that have fixed values are called
constant, while quantities like x, y, z that can take
arbitrary values are called variables. An algebraic
equation is an equation containing some variables and
constants. The problem is usually to find the values of
the variables that satisfy the equation(s).
i. Multiply each term of an equation by a non-zero
constant.
ii. Subtract (or add) a constant from both sides of an
equation
iii. Subtract (or add) one equation from another

3. ALGEBRAIC EQUATIONS
• Linear Equations
• A linear equation has the form ax+b=0. where
a, b are constants and x is variable.
• To solve, subtract b from both sides to get
ax = -b
then divide both side by a to get x = - b/a
This is then the solution of the equation.

4. ALGEBRAIC EQUATIONS
• Linear Equations
• More example on the explanation of linear
equation.
• Solve 3x – 12 = 0
Solution
3x-12 = 0
3x = 12
x = 12/3 = 4

5. ALGEBRAIC EQUATIONS
• Quadratic Equations
• A quadratic equation contains x2 . it has the
form:
• A quadratic equation can be solved by
a) factorization method (b) completing squares
c) the graphical method.
d) the use of quadratic formula

6. ALGEBRAIC EQUATIONS
• Quadratic Equations
• Example; solve the equation by (a)
factorization method (b) completing squares (c) the use
of quadratic formula (d) use of graphs.
• Solution
• (a)
•

7. ALGEBRAIC EQUATIONS
• Quadratic Equations
• (b)
Add and subtract

8. ALGEBRAIC EQUATIONS
• Quadratic Equations
(c)

9. ALGEBRAIC EQUATIONS
• Quadratic Equations
• (d) For the graphical method, we draw the
graph of and note values
of x when y = 0. i.e where the graph meets the
x-axis.

10. ALGEBRAIC EQUATIONS
• Quadratic Equations
• From the graph, y = 0 when x = -4 or x = 2.5
• The solution of the equation is x = -4 or 2.5

11. ALGEBRAIC EQUATIONS
Simultaneous Equations
• Simultaneous equations involve two or more
equations contain two or more variables. The
methods of solution is to eliminate some of
the variables. Solve for one variable and then
substitute its value in the equations. This
method progressively reduces the number
variables and eventually leads to a solution(if
a solution exists)

12. ALGEBRAIC EQUATIONS
Simultaneous Equations
Example: solve for x and y in

13. ALGEBRAIC EQUATIONS
Using elimination method, first we eliminate x
then y
Substituting this in equation(1) we get