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

Parabola, If the point (a,2a) is an interior point of the region bounded by...

If the point (a,2a) is an interior point of the region bounded by the parabola y2=16x and the double ordinate through the focus then a belongs to

Indices, What is a way to solve indices

What is a way to solve indices

Describe the introduction to integers, Describe the Introduction to Integer...

Describe the Introduction to Integers ? Integers include the positive and negative whole numbers, such as -4, -3, -2, -1, 0, 1, 2, 3, 4, and so on. A negative number has a "

Calculate the slope of the line, Calculate the slope of the line: Exa...

Calculate the slope of the line: Example: calculate  the  slope  of  the  line  whose  equation  is  y  =  2x  +  3  and  whose y-intercept is (0,3). Solution:    y =

Factorization example, Example  Factorize x 2 - 4x + 4. If ...

Example  Factorize x 2 - 4x + 4. If we substitute x = 1, the value of the expression will be (1) 2 - 4(1) + 4 = 1 If we substitute x = -1, the value o

Prime factors, I need help with prime factors.

I need help with prime factors.

Method of cylinders or method of shells, Method of cylinders or method of s...

Method of cylinders or method of shells The formula for the area in all of the cases will be,                                                        A = 2 ∏ ( radius ) (heig

Trig, I need help with this question: Find the probability that two quarter...

I need help with this question: Find the probability that two quarters and a nickel are chosen without replacement from a bag of 8 quarters and 12 nickles.

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