linear equation and quadratic equation

Today we learn about linear equation and quadratic equation

General form from linear equation and quadratic equation write to a, b, p, q, and r constitute real number.

y = ax + b (linear equation), but y = px² + qx + r (quadratic equation)

there is several steps to determine association from solution linear equation and quadratic equation :  

1.      Substitute linear equation y = ax + b to quadratic equation y = px² + qx + r

so ax + b = px² + qx + r

move part of equation in order to same 0 and the value of  x² is not negatif because can be more easy to determine the value of x.

px² + (q – a)x + (r – b) = 0, for get the value of x we can use factorization or we can use ABC formula. After we get the value of x, so we substitute to linear equation y = ax + b or to quadratic equation y = px² + qx + r, so we can get the value of y. value (x,y) constitute solution association of linear equation and quadratic equation.

2.       For determining quantity association of linear equation and quadratic equation. We can use discriminant. 

If the value of  D = 0, so the association of linear equation and quadratic equation is one

If the value of D > 0, so the solution have 2 association.

But if the value D < 0, so measure up to imaginary association

For example : equation y = 2x + 1 and y = x² + x -5

the value of a = 2, b = 1, p = 1, q = 1, r = -5

1.       We substitute it so be 2x + 1 = x² -3 x -5

Move part of equation, x² + ((-3)-2)x + ((-5) -1) = 0

x²  - 5x - 6 = 0

(x - 6 ) (x + 1) = 0

so x₁ = 6, x₂ = -1

2.       Then the value of x substitute to the equation

y = 2 (6) + 1           y = 2 (-1) + 1         y = (6)² - 3 (6) - 5          y = (-1)²  - 3 (-1) -5

y = 13                     y = -1                      y = 13                             y = -1

so the solution of association  ={(6, 13), (-1, -1)}

for the clear of my explanation you can watch the video, click the video  

source: (click here)                                                      source: (click here)
After you watch the video you can  understand more how to determine the solution of linear equation and quadratic equation.

1. Graph Methods


a. Drawing graphs with dot method intercept
b. When two lines intersect at one point obtained a member of the (x, y)
c. When these two parallel lines (not intersected it) then it cannot be obtained members of the set of completion
d. When the two lines coincide then obtained settlement that is not set infinity


2. Substitution method
Replace a variable with a variable from the other equations


3. Elimination method
Eliminating one variable
Prior to this study is completed there is a matter for you to do, with regard to systems of linear and quadratic equations.

Namely:

1. the equation y =-x + 2 and y = x2 + 10-10

2. The equation y =-3x - 6 and y = x2 + 4x + 6

send your answer to my email (ita.pertiwi @ sampoernaeducation.net)

safe work and spirit

 picture