Introduction to substitution elimination method:
These methods are been used to calculate the unknowns involved in different equations. Mathematically speaking, we need at least n number of equations, if there involved n unknowns. Here, let us discuss the substitution elimination method to solve simultaneous equations of two unknowns.
Between, if you have problem on these topics solve by the substitution method, please browse expert math related websites for more help on solving equation.
Example on Substitution Elimination Method:
Ex 1: Solve the following equations using elimination method:
x + 2y = 10
x – y = 4
Sol: Here let us call the equations as 1 and 2.
x + 2y = 10 ---------`->` (1)
x – y = 4 ------------`|->` (2)
(2) × 2 `rArr` 2x – 2y = 8
(+) (1) `rArr` x + 2y = 10
`rArr` 3x = 18
`rArr` x = `(18)/(3)` = 6
`rArr` x = 6
Now plug in x = 6 in the equation number (1) as follows:
x + 2y = 10 `rArr` 6 + 2y = 10
`rArr` 2y = 10 - 6 = 4
`rArr` y = `(4)/(2)` = 2.
`rArr` y = 2
Therefore, the solution of the given equations are x = 6, y = 2.
Example on Substitution Elimination Method
Ex 2: Solve the following equations using substitution method
x + 2y = 10
x – y = 4
Sol: Here let us call the equations as 1 and 2.
x + 2y = 10 ---------`|->` (1)
x – y = 4 ----------`|->` (2)
(2) `rArr` y = x – 4 --`|->` (3)
Now, substitute y = x – 4 in (1), we get as follows:
x + 2y = 10 `rArr` x + 2 (x – 4) = 10
`rArr` x + 2x – 8 = 10
`rArr` 3x = 10 + 8 = 18
`rArr` x = 18/3
`rArr` x = 6
Now plug in x = 6 in the equation number (3) as follows:
y = x – 4 `rArr` y = 6 – 4 = 2
`rArr` y = 2
Therefore, the solution of the given equations are x = 6, y = 2.
Practice Problems on Substitution Elimination Method
Solve the following equations using substitution elimination method:
1. 3x + 2y = 23
x – y = 1
Answer: x = 5, y = 4.
2. 2x + y = 21
x + y = 15
Answer: x = 6, y = 9.
My Previous Blog :- http://advancemath.blogspot.in/2012/10/perimeter-semi-circle.html
These methods are been used to calculate the unknowns involved in different equations. Mathematically speaking, we need at least n number of equations, if there involved n unknowns. Here, let us discuss the substitution elimination method to solve simultaneous equations of two unknowns.
Between, if you have problem on these topics solve by the substitution method, please browse expert math related websites for more help on solving equation.
Example on Substitution Elimination Method:
Ex 1: Solve the following equations using elimination method:
x + 2y = 10
x – y = 4
Sol: Here let us call the equations as 1 and 2.
x + 2y = 10 ---------`->` (1)
x – y = 4 ------------`|->` (2)
(2) × 2 `rArr` 2x – 2y = 8
(+) (1) `rArr` x + 2y = 10
`rArr` 3x = 18
`rArr` x = `(18)/(3)` = 6
`rArr` x = 6
Now plug in x = 6 in the equation number (1) as follows:
x + 2y = 10 `rArr` 6 + 2y = 10
`rArr` 2y = 10 - 6 = 4
`rArr` y = `(4)/(2)` = 2.
`rArr` y = 2
Therefore, the solution of the given equations are x = 6, y = 2.
Example on Substitution Elimination Method
Ex 2: Solve the following equations using substitution method
x + 2y = 10
x – y = 4
Sol: Here let us call the equations as 1 and 2.
x + 2y = 10 ---------`|->` (1)
x – y = 4 ----------`|->` (2)
(2) `rArr` y = x – 4 --`|->` (3)
Now, substitute y = x – 4 in (1), we get as follows:
x + 2y = 10 `rArr` x + 2 (x – 4) = 10
`rArr` x + 2x – 8 = 10
`rArr` 3x = 10 + 8 = 18
`rArr` x = 18/3
`rArr` x = 6
Now plug in x = 6 in the equation number (3) as follows:
y = x – 4 `rArr` y = 6 – 4 = 2
`rArr` y = 2
Therefore, the solution of the given equations are x = 6, y = 2.
Practice Problems on Substitution Elimination Method
Solve the following equations using substitution elimination method:
1. 3x + 2y = 23
x – y = 1
Answer: x = 5, y = 4.
2. 2x + y = 21
x + y = 15
Answer: x = 6, y = 9.
My Previous Blog :- http://advancemath.blogspot.in/2012/10/perimeter-semi-circle.html
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