This powerpoint presentation discusses or talks about the topic or lesson System of Equations involving Quadratic Equations. It also discusses and explains the rules, steps and examples of System of Equations involving Quadratic Equations

1. System of Equations
involving Quadratic
Equations

2. The equations:
Form a system of equation called quadratic
system
a . b = 36
a2 + b2 = 97

3. It involves at least one quadratic equations.
Quadratic-Linear – at least one linear
equation
Quadratic-Quadratic – at least two
quadratic equations
Quadratic System

4. A system of equations which consists
of a linear equation and quadratic
equation has two roots while a system
of equations which consists of two
quadratic equations usually have four
roots
Quadratic System

5. 1. Graphing
2. Substitution
3. Linear combination
Ways on Solving
Quadratic System

6. There are no fixed procedures in solving a
system of equations involving quadratic
equations but oftentimes, the target is to
find the values of any of the following
expressions:
(x + y, x – y and xy)
From which the value of x and y can be
obtained

7. Solution: Use the substitution method to solve
the system by rewriting:
Equation 2: Thus, y = 10 – 2x
Example:
4x2 + y2 = 52
2x + y = 10

8. Solution (for x):
4x2 + y2 = 52
4x2 + (10-2x)2 = 52 Replace y with 10-2x
4x2 + 100 – 40x + 4x2 = 52 Simplify
8x2 – 40x + 48 = 0 Combine like terms
x2 – 5x + 6 = 0 Divide both sides by 4
(x-3) (x-2) = 0 Factor
x – 3 = 0 or x – 2 = 0
x = 3 x = 2

9. Solution (for y):
If x = 3 If x=2, then
y = 10 – 2(3) y = 10 – 2(2)
y = 4 y = 6
The solutions of the system of equations are
(3,4) and (2,6)