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

Sqares, Recently I had an insight regarding the difference between squares ...

Recently I had an insight regarding the difference between squares of sequential whole numbers and the sum of those two whole numbers. I quickly realized the following: x + (x+1)

Scale Drawing, Model of 180 meter tall building using a scale of 1.5 centim...

Model of 180 meter tall building using a scale of 1.5 centimeters = 3.5 meters. How tall will the model be?

Cardioids and limacons - polar coordinates, Cardioids and Limacons Thes...

Cardioids and Limacons These can be split up into the following three cases. 1. Cardioids: r = a + a cos θ and r = a + a sin θ. These encompass a graph that is vaguel

Initial conditions and boundary conditions, Initial Condition...

Initial Conditions and Boundary Conditions In many problems on integration, an initial condition (y = y 0 when x = 0) or a boundary condition (y = y

Describe graphing equations with a positive slope, Describe Graphing Equati...

Describe Graphing Equations with a Positive Slope? There are 3 steps to graphing a linear equation: 1. Identify and plot the y-intercept. 2. Determine the slope. Use the slope

Determine the domain and range of function, Determine the domain of each of...

Determine the domain of each of the following functions.                         f( x ) = x - 4 / x 2 - 2 x -15 Solution With this problem we have to avoid division by

Area in polar cordinates, find the area of the region within the cardioid r...

find the area of the region within the cardioid r=1-cos

Find the probability distribution of x, If a pair of dice is thrown and X d...

If a pair of dice is thrown and X denotes the sum of the numbers on them. Find the probability distribution of X.Also find the expectation of X.     SOLUTION:    In a singl

Integration, ((1/x^1/2-(x-1)^1/2)+(1/(5-3(x-1)^2)^1/2)

((1/x^1/2-(x-1)^1/2)+(1/(5-3(x-1)^2)^1/2)

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