Method for simultaneous equations of two or more variables, Mathematics

Assignment Help:

Method

In this method we eliminate either x or y, get the value of other variable and then substitute that value in either of the original equations to get the value of the other variable. Let us look at it.

We are given two equations 3x + 4y = 10 and 4x + y = 9. We write them as follows.

      3x + 4y = 10                                       ........(1)

      4x + y  = 9                                         ........(2)

In this example, let us eliminate y. Multiply equ. (2) by 4. We have

      4(4x + y = 9)

which is   16x + 4y = 36                             ........(3)

We observe that the coefficients of y in equations (1) and (3) are one and the same, and therefore, we subtract equ.(1) from equ.(3).

16x + 4y = 36   

- (3x + 4y = 10) 


13x + 0  = 26   


At this point one should remember that the signs of equation (1) should be changed before subtracting.

      13x      = 26

          x  = 26/13 = 2

We now substitute the value of x = 2 in either equ. (1) or (2). Let us substitute in equ. (2).

      4x + y      =   9

      4(2) + y    =   9

      8 + y        =   9

      y = 9 - 8   =   1

That is, the values of x and y for which both the equations are satisfied are x = 2 and y = 1.

We substitute these values in equ. (1) and check.

      3x + 4y       =   10

      3(2) + 4(1)  =   10

      6 + 4          =   10

      10              =   10

That is, LHS = RHS.


Related Discussions:- Method for simultaneous equations of two or more variables

Math, #question.help.

#question.help.

What is the maximum volume of rectangular box, 1. A rectangular piece of ca...

1. A rectangular piece of cardboard measuring 26 inches by 42 inches is to be made into a box with an open top by cutting equal size squares from each comer and folding up the side

Normal Distribution, You don''t have to give me the answer. I just want to ...

You don''t have to give me the answer. I just want to know HOW to do it. In a set of 400 ACT scores where the mean is 22 and the standard deviation is 4.5, how many scores are ex

Divergence test - sequences and series, Divergence Test Once again...

Divergence Test Once again, do NOT misuse this test.  This test only says that a series is definite to diverge if the series terms do not go to zero in the limit.  If the

Holistic marketing , Necessity of holistic marketing or importance of holis...

Necessity of holistic marketing or importance of holistic marketing

Use the definition of the right- and left-handed limits, Use the definition...

Use the definition of the limit to prove the given limit. Solution Let ε> 0 is any number then we have to find a number δ > 0 so that the following will be true. |

How many permutations of the letters a b c d e f g h, How many permutations...

How many permutations of the letters A B C D E F G H consist of string DEF?    Ans: It is the dilemma of finding number of words that can be formed along with the given 8 lette

Bricklayer estimates 6.5 how many bricks will he required, A bricklayer est...

A bricklayer estimates that he requires 6.5 bricks per square foot. He needs to lay a patio that will be 110 square feet. How many bricks will he required? Multiply 6.5 by 110;

One integer is two more than another what is greater integer, One integer i...

One integer is two more than another. The sum of the lesser integer and double the greater is 7. What is the greater integer? Let x = the greater integer and y = the lesser int

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd