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Two Simple Methods of Solving Simultaneous Equations With Two Variables
When solving a simultaneous equation in two variables, we try to find the values of the two variables that occur in the given set of equations. Before we try to go any further, we should define what simultaneous equations in two different variables are. A simultaneous equation in two variables is a set of two equations that have two variables, such as x and y. For example, this is the simultaneous equation x+2y= 3, x-4y= 5. So it can be seen that we have two different equations, but with two different variables x and y. Now there are two simple methods to solve the simultaneous equation. They are substitution method and elimination method.
Replacement method. A method of substitution is one that uses a change of subject of an equation principle to find the value of two given unknown variables. This is best illustrated by a working example. Solve these equations using the substitution method x+4y= 5, x-5y= 4.
First, we call Eqs
x+4y= 5…………….(1.)
x-5y= 4……………….(2.)
Second, from (2.), make x the subject of the equation,
x-5y= 4, which makes x the object of the equation,
we have x= 4+5y.
Then we replace x in (1.),
therefore from (1.) x+4y= 5 we get
(4+5y)+4y=5
4+9y = 5
y = 1/9.
Now we substitute y in (2.) to find the value of x.
Therefore, from (2.),
x-5y = 4 and y = 1/9
x-5(1/9) = 4
x = 41/9.
So x = 41/9 and y = 1/9.
There we see that the replacement method is the same throughout. Click here to learn more about this method.
Method of elimination.
The method of elimination is almost the same as the method of substitution, but there are some differences. Let’s explain this using the previous example. Solve these equations using x+4y= 5, x-5y= 4.
Let’s start by naming the equations
x+4y= 5…………….(1.)
x-5y= 4……………….(2.) Now we continue with (2.) subtracting (1.). So x+4y= 5 – x-5y= 4 to get 9y= 1 y= 1/9 This step is the main difference between elimination method and substitution method. Next, we find the value of x by substitution. in that year (1.). So from (1.) we have x+4y= 5, but y=1/9so x+4(1/9)= 5 x+4/9= 5 x= 41/9So the elimination method of solving the equation simultaneously is using the substitution method. For more information on the removal method, click here. It can be noted that the answers are the same using the substitution method and the elimination method to solve the same simultaneous equation. But this is not always the case.
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