Simultaneous equations with two or more than two variables, Mathematics

Assignment Help:

Method to solve Simultaneous Equations with two or more than two variables

Method 

Above we have seen equations wherein we are required to find the value of the variable x only. Apart from the equations of the type we have seen above, simple equations of the form 7x + 2y = 47 also exists. As against the equations x - 3 = 12 or 3x + 5 = 20 where we had a single variable x, we have two variables x and y. If we express this equation in terms of y it will be

                   7x + 2y                = 47

                   7x - 7x + 2y          = 47 - 7x

                   0 + 2y                  = 47 - 7x

                    2y                      = 47 - 7x

               1407_simultaneous equation.png

In this expression by giving values to x and solving the expression we get corresponding values for y.

Now if another equation of the form 5x - 4y = 1 is expressed in terms of y, we have

y

= 593_simultaneous equation1.png

For this equation also if we substitute values for x, we would get corresponding values for y.

At this stage if we want values which satisfy both the equations then the values of y in both these equations should be identical. That is,

2040_simultaneous equation2.png



On cross multiplying, we have 4(47 - 7x) = 2(5x - 1)

                   188 - 28x = 10x - 2

Collecting all x terms and constants, we have

                 -10x - 28x    =    - 2 - 188

                         -38x    =    - 190

                              x    =       5

We substitute this value of x = 5, in either of equations to get the value of y.

                   5x - 4y     =     1

                   5(5) - 4y  =     1

                   - 4y         =     1 - 25

                   - 4y         =       - 24

                       y         =       -24/ - 4 = 6.

Therefore, the common values of x and y which satisfy these two equations simultaneously are x = 5 and y = 6. Therefore, we can define simultaneous equations as two or more equations which are satisfied by the same values of x and y (unknown quantities). 


Related Discussions:- Simultaneous equations with two or more than two variables

Find the length of the rectangle, Suppose that the width of a rectangle is ...

Suppose that the width of a rectangle is three feet shorter than length and that the perimeter of the rectangle is 84 feet. a)    Set up an equation for the perimeter involving

Show basic trigonometric functions, Q. Show basic Trigonometric Functions? ...

Q. Show basic Trigonometric Functions? Ans. There are six trigonometric functions and they can be defined using a right angle triangle. We first label each side according

Application of linear equations, Application of Linear Equations We ar...

Application of Linear Equations We are going to talk about applications to linear equations.  Or, put in other terms, now we will start looking at story problems or word probl

Math homework help, I need help witth my homework can you help please

I need help witth my homework can you help please

Parent, Sam has 18 marbles. Dean has 3 marbles. Dean has ---- as many marbl...

Sam has 18 marbles. Dean has 3 marbles. Dean has ---- as many marbles as Sam?

Math, i have problems with math and my teacher said that i am still progres...

i have problems with math and my teacher said that i am still progressing in math

Permission for xii class, Is there any class in expertsmind for second year...

Is there any class in expertsmind for second year english.?

Each child is unique in learning development, Each Child Is Unique :  Alth...

Each Child Is Unique :  Although every child goes through similar stages of development, the process may vary from one set of children to another, and also from one child to anoth

What is congruent angles in parallel lines, What is Congruent Angles in Par...

What is Congruent Angles in Parallel Lines ? Postulate 4.1 (The Parallel Postulate) Through a given point not on a line there is exactly one line parallel to the line. T

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