Method for simultaneous equations of two or more variables, Mathematics

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.

Posted Date: 9/13/2012 3:55:09 AM | Location : United States







Related Discussions:- Method for simultaneous equations of two or more variables, Assignment Help, Ask Question on Method for simultaneous equations of two or more variables, Get Answer, Expert's Help, Method for simultaneous equations of two or more variables Discussions

Write discussion on Method for simultaneous equations of two or more variables
Your posts are moderated
Related Questions
Find the sum of a+b, a-b, a-3b, ...... to 22 terms. Ans:    a + b, a - b, a - 3b, up to 22 terms d= a - b - a - b = 2b S22 =22/2 [2(a+b)+21(-2b)] 11[2a + 2b - 42b] =

A bank pays on its savings an interest rate of 6% per year but compounds interest monthly (i.e., estimates the interest each month and adds it to the balance).  You plan to deposit

We have seen that if y is a function of x, then for each given value of x, we can determine uniquely the value of y as per the functional relationship. For some f

Elliptic Paraboloid The equation which is given here is the equation of an elliptic paraboloid. x 2 /a 2 + y 2 /b 2 = z/c Like with cylinders this has a cross section

Eddie mkes $15.75 per hour. Estimate how much Eddie will make per year if he works 40 hours per week and 50 weeks per year.

The area of Mr. Smith's rectangular classroom is x 2 - 25. Which of the following binomials could represent the length and the width of the room? Since area of a rectangle is

DISTINCT EIGENVALUES -SYSTEM SOLVING : E xample Solve the following IVP. Solution : Therefore, the first thing that we must to do that is, get the eigenvalues

Explain Identifying Conic Sections The graph of a quadratic equation in the variables x and y, like this one, x 2 + 3y 2 + 6y = -4, is a conic sections. There are three kind

1) find the maxima and minima of f(x,y,z) = 2x + y -3z subject to the constraint 2x^2+y^2+2z^2=1 2)compute the work done by the force field F(x,y,z) = x^2I + y j +y k in moving

Standard Hypothesis Tests In principal, we can test the significance of any statistic related to any type of probability distribution. Conversely we will be interested in a few