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Simultaneous Equations are a set of equations containing multiple variables. This set is referred to as a system of equations. Simultaneous Equations and System of Equations are those equations where two or more variables are related to each other through an equal number of equations. In order to find the solution the provided equations have to be utilized to find the value of each variable.
The simplest form of simultaneous equations in two unknown numbers is x and y.
Consider 4x + y = 9
And 3x = 6.
There are two unknown variables x and y. Here it is given that 3x = 6, then we can say that x = 6/3, which is 2. Therefore, x = 2.
Substituting the value of x we get,
4 *2 +y = 9
8+y = 9
Therefore y = 9-8 = 1.
Y= 1.
The whole solution is therefore x=2 and y=1.
Consider, x+y = 4 (a)
x-y = 2 (b)
Now, if we add the left hand side of (a) to the left hand side of (b) and the right hand side of (a) and right hand side of (b).
x+y+x-y = 4+2
2x = 6
Therefore x = 3. Now we can deduce the value of y through x.
x+y = 4.
3+y= 4.
And y= 4-3 =1.
So, the values of x and y are 3 and 1 respectively.
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"Higher order simultaneous equation where I needed to find out values for 5 or 6 variables forming appropriate equations from a given problem, was really my weak area. However, when I came across HwA they helped me and also assisted me to understand how exactly from a problem statement, the equations can be formed and how they can be evaluated". -Bobby Thatcher
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