In mathematics, simultaneous equations are a set of equations containing multiple variables. This set is often referred to as a system of equations. A solution to a system of equations is a particular specification of the values of all variables that simultaneously satisfies all of the equations. (Source from Wikipedia)Here we are going to learn about how to solve the simultaneous equations and its example problems
There are many methods to solving a simultaneous equation. They are following,
Elimination method
Substitution method
Graphical method
Matrix method
Here we are using two methods elimination and substitution method
Ex : Solve the following simultaneous equation using elimination method,
2x+y=8
x+y=6
Sol : First we have to solve the equation using elimination method
2x+y=8 ……………….1
x+y=6 ………………….2
Multiply equation 2 by 2
Then the equation will be
2x+2y=12 ……………..3
Subtract the equation 2 from equation 1 we get
-y = -4
Therefore the value of y = 4
Substitute y value in equation 2
x+4=6
Add both sides -4 we get
x+4-4 = 6-4
x=2
Therefore solution of given simultaneous equation is x = 2, y = 4
Ex 2: Solving simultaneous equation using elimination method
Take the same equation, that is
2x+y=8
x+y=6
Sol : Here we are using elimination method of solving let as assume,
2x+y=8 ……………….1
x+y=6 ………………….2
From the equation 2
x + y =6
Add both sides –y
X+y-y=6-y
X=6-y ……………………3
Form the above x value substitute in the equation 1 we get
2x+y=8
2 (6-y) + y = 8
12-2y+y=8
12-y=8
Add both sides -12 we get
12-12-y=8-12
Left hand side 12 -12 will be cancel
-y=-4
Therefore the y value is 4
Now we substitute y value into the equation 3 we get
x = 6-y
x = 6-4
x=2
Therefore the value of x=2
So solution of given simultaneous equation is x=2 ,y=4