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

Rate -categories of multiplication, Rate - when we know how many objects...

Rate - when we know how many objects are in a set, and need to find out the total number in several copies of that set. (e.g., if a child uses 4 copybooks in a year, how many co

Matrices, suppose you a business owner and selling cloth. the following rep...

suppose you a business owner and selling cloth. the following represents the number of items sold and the cost for each item. use matrix operation to determine the total revenue ov

Average cost function, Average cost function : Now let's turn our attentio...

Average cost function : Now let's turn our attention to the average cost function. If C ( x ) is the cost function for some of the  item then the average cost function is,

Polynomial : f(x).f(1/x), A polynomial satisfies the following relation f(x...

A polynomial satisfies the following relation f(x).f(1/x)= f(x)+f(1/x). f(2) = 33. fIND f(3) Ans) The required polynomial is x^5 +1. This polynomial satisfies the condition state

Permutations and combinations, How many arrangements can be made from the l...

How many arrangements can be made from the letters of the word " VENUS " such that the order of the vowels remains the same?

Trignometry, Define the given satatement : 1.sin90-sin89=sin10 using pythag...

Define the given satatement : 1.sin90-sin89=sin10 using pythagoras theoram 2. How can any value of sin and cosis always given any value of cosec.

What is the square root of -i and argument of -i, What is the square root o...

What is the square root of -i and argument of -i Ans) argument of -i is 270 ad 1 is the square root of -i

determine that the relation is symmetric and transitive, 1. Let R and S be...

1. Let R and S be relations on a set A. For each statement, conclude whether it is true or false. In each case, provide a proof or a counterexample, whichever applies. (a) If R

Quadratic equations, Q UADRATIC EQUATIONS: For  the  things  of this  wor...

Q UADRATIC EQUATIONS: For  the  things  of this  world  cannot  be  made  known without  a  knowledge of mathematics. Solve by factorization a.    4x 2 - 4a 2 x +

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