Matematicas Basicas

Algebra:
Simultaneous Equations
-Ger rid of x or y
-Solve for one variable
-Substitute

6x+9y=15
3x+5y=8
In this case, multiply the second equation by 2 to get 6x as well.
6x+10y=16-6x+9=15
Then subtract the top one from the second one to get rid of the x.
y=1
Then substitute y with your result to find x.
3x+5=8
3+5=8
So x=1 and y=1.
Solve the simultaneous equations by drawinggraphs.
y = 2x +1
y = x2 - 2

You can also solve simultaneous equations when one is a quadratic without a graph.
y=x^2+3x-5
y=2x+1
To solve this first you need to make them equal.
x^2+3x-5=2x+1
Then you need to make that equal cero.
x^2+3x-2x-5=2x-2x+1
x^2+x-5-1=1-1
x^2+x-6=0
Then you finish with a simple quadratic equation that you can solve either with the quadratic formula orin your mind.
(x+3) (x-2)
x=-3,x=+2
Remember that you must have your mind open to every tricky question. This is an odd example of a simultaneous equation:
x^2+y^2+xy+x=30
y=2x-3
With this you would assume that you must make them equal but that’s not true. On the second equation you are told what does y equals so you need to substitute it for all the ys in the first equation.x^2+〖(2x-3)〗^2+x(2x-3)+x=30
x^2+(2x-3)(2x-3)+〖2x〗^2-3x+x=30
x^2+〖4x〗^2-6x-6x+9+2x^2-3x+x=30
7x^2-14x+9=30
Now that you have a simple quadratic equation you need to make it equal to cero.
7x^2-14x+9-30=30-30
7x^2-14x-21=0
To get rid of the number 7 after the x square you need to find a common denominator to divide everything.
7(x^2-2x-3)
And divide all by 7. Now you get a nice and simple equation.
x^2-2x-3(x-3)(x+1)
Solved. Bam it’s On.

Factorising
Factorising is putting an equation into brackets. Some equations will be factorised in one bracket but others in two. Quadratics will always be factorised into two brackets.
4x-6
For factorising this equation first you need to find a common denominator. In this case it will be 2. The common denominator will be outside the bracket and thesimplified numbers inside.
2(2x-3)
Some times you will have a variable outside the brackets.
8m^2+12m
2m(4m+6)

When factorising quadratics, the method is different.
x^2+5x+6
First you know that both brackets will be x+?. For finding ?, you need to find a number that adds 5 and multiply 6. Remember that adds the one with the x next to it and multiply the last number. In this case 2 and 3.(x+2)(x+3)
Quadratics.
All quadratics have the same structure. ax^2+bx+c=0
When you are asked to factorise quadratics it refers to do the thing above.
When you are asked to solve a quadratic equation, you need to find x.
The formula for solving quadratic equations is the following:
x=(-b±√(b^2-4ac))/2a
To use this equation in the calculator you can’t just type it and that’s all, you need tofollow some steps before. Supposing that you are given the following quadratic equation:
x^2+7x-44=0
First you need to feet it in your formula.
x=(-7±√(7^2-4×-44))/2
Then you need to find out what is inside the square root, so you find the square of 7 and multiply 4x-44. Since 4 is positive and -44 is negative, they will multiply a negative number that will be -176. Then you’ll get:x=(-7±√(49--176))/2
The double – indicates that it will be a + so you add 49 to 176 that gives you 225. Then you need to find out the square root of 225.
x=(-7±√225)/2 =(-7±15)/2
Now you just need to add or subtract 15 to -7 and divide by 2. The answer for this is -11 and 4.

Algebraic fractions.
To solve algebraic fractions is quite easy. It is like solving a normal fraction but with algebraicterms.
(x-3)/4+4/(x-3)
This is a classic exam algebraic fraction QUESTION. At first sight you imagine that you just need to add the top ones and the bottom ones but you don’t realize that it is the same as a simple fraction addition. To solve an addition with factions remember that you must make sure that the numbers under are the same, a common denominator. For this you can simply multiply...