More than one variable linear equations

Shortcut tricks on more than one variable linear equations are one of the most important topics in exams. Time takes a huge part in competitive exams. If you manage your time then you can do well in those exams. Most of us skip that part. Here in this page we give few examples on More than one variable linear equations shortcut tricks. We try to provide all types of shortcut tricks on more than one variable linear equations here. We request all visitors to read all examples carefully. These examples here will help you to better understand shortcut tricks on more than one variable linear equations.

Before doing anything we recommend you to do a math practice set. Write down twenty math problems related to this topic on a page. Do first ten maths using basic formula of this math topic. You also need to keep track of Timing. After finish write down total time taken by you to solve those ten maths. Now practice our shortcut tricks on more than one variable linear equations and read examples carefully. After finishing this do remaining questions using More than one variable linear equations shortcut tricks. Again keep track of Timing. This time you will surely see improvement in your timing. But this is not enough. If you need to improve your timing more then you need to practice more.

Math section in a competitive exam is the most important part of the exam. It doesn’t mean that other topics are not so important. But only math portion can leads you to a good score. A good score comes with practice and practice. All you need to do is to do math problems correctly within time, and only shortcut tricks can give you that success. But it doesn’t mean that you can’t do math problems without using any shortcut tricks. You may have that potential to do maths within time without using any shortcut tricks. But so many people can’t do this. So More than one variable linear equations shortcut tricks here for those people. Here in this page we try to put all types of shortcut tricks on More than one variable linear equations. But it possible we miss any. We appreciate if you share that with us. Your little help will help so many needy.

More than one variable linear equations

A Linear equations is a mathematical equation where the power of any constant unknown variable is always one and the variable has one or more than one is known as linear equations.

Example: ax2 + bx + c = 0
it is equal to 0 and the a , b , c are the constant value and we can say that x represent as unknown.

The a, b, c are the constant and coefficient or linear coefficient. Quadratic equation hold the only power of x which is also non negative integer.

Example: 6x2 + 8y + 2z = 0 here is 6, 8, 2 are constant value. and x is the unknown variable.

 

Solve of More than one variable linear equations.

  • 5x + 2y =6 Equation no 1.
  • 8x + 4y =4 Equation no 2.

5x + 2y =6 x 4…..eq1
8x + 4y =4 x 2…..eq2

At first we multiply the equation no 1 and 2 by 4 and 2. than the obtain equation is 20x + 8y = 24 and 16x + 8y = 8,
Subtract eq1 from eq2.
So we get 4x = 16 , x = 4.
and now we put the x value into eq1 and get the value of y so 5(4) +2y = 6, 20 + 2y = 6, 2y = -20 + 6, so,
y = -14 / 2 = -7
and so x = 4  and y = -7.

 

Example 1:
6 x2 + 10x + 4 = 0 ………Equation 1
4y2 + 12y + 8 = 0 ……….Equation 2

Answer :
Shortcut tricks :
6  x 4 = +24
we break + 24 in two parts such that addition between them is 10.
+32 = (+6) + (+ 4) = +10 .
Change sign of both factor and divide by cofficient of x2 ,
So ,  -6 /  6 = -1 .
– 4 / 6 = -2 / 3 .

Similarly ………..
4  x 8 = +32
we break + 32 in two parts such that addition between them is 12.
+32 = (+8) + (+ 4) = +12 .
Change sign of both factor and divide by cofficient of y2 ,
So -4 /  8 = -1 / 2 .
– 4 / 4 = -1 .

X = -1 , – 2 / 3 .
Y = -1  , -1 / 2 .

 

 

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