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In elimination method _____________ is an important condition.
- a)Equating either of the coefficients
- b)Equating only the y coefficient.
- c)Equating only the x co-efficient.
- d)Equating both the coefficients.
Correct answer is option 'A'. Can you explain this answer?
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In elimination method _____________ is an important condition.a...
Elimination Method (by Equating Coefficients)
There is another method of eliminating a variable, than often used method i. e --------Suppose you are to solve
23x - 17y + 11=0 ------(1)
and 31x + 13y - 57 = 0 -------(2)
Now expressing x in terms of y would involve division by 23 or 31. Express y in terms of x, it would involve division by 17 or 13. You know that multiplication is more convenient than division, better to convert the division process into a multiplication process.
Multiplying the first equation by 13 viz., coefficient of y in (2), and second by 17 viz., coefficient of y in (1), you will get an equivalent system of equations. The new system has the advantage that y has the same numerical coefficient 17x13 in both the equations. When you add these new equations, the terms containing y would cancel out as these have opposite signs and the same numerical coefficient. Thus, y has been eliminated. Now proceed as before, and solve the system. This method of elimination is also called elimination by equating coefficients for obvious reasons.
Example: Solve the following system of equations using the elimination method by equating coefficients:
11x - 5y + 61 = 0 (1)
3x - 20y - 2 = 0 (2)
Solution: Let us multiply equation (1) by 3 and equation (2) by 11. This gives
33x - 15y + 183 = 0 (3)
and 33x - 220y - 22 = 0 (4)
Subtracting (4) from (3), you will get 205y + 205 = 0
, or y = - 1
Substituting this value of y in equation (2), you will get
3x - 20 * (- 1) - 2 = 0
or 3x = -18
or x = - 6
Thus, the required solution is
x = - 6 and y = -1.
Now you should verify; substitute x = - 6 and y = -1 in the given equations, you will notice both the equations are satisfied. Hence, the solution is correct
Most Upvoted Answer
In elimination method _____________ is an important condition.a...
Equating coefficients is an important condition in the elimination method
Elimination method in solving systems of linear equations involves eliminating one variable by adding or subtracting the equations. In order to successfully apply this method, it is crucial to equate either of the coefficients. Here's why:
Why equating coefficients is important:
- When we equate the coefficients of either x or y in the two equations, we can easily eliminate one variable by adding or subtracting the equations.
- This ensures that the resulting equation after elimination will have only one variable, making it easier to solve for that variable.
- Equating coefficients helps simplify the process of solving the system of equations and reduces the chances of making errors.
Example:
Let's consider the following system of equations:
2x + 3y = 7
4x - 5y = 1
To eliminate y, we need to equate the coefficients of y in the two equations. In this case, we can multiply the first equation by 5 and the second equation by 3 to get:
15y = 35
-15y = 3
By adding these two equations, we eliminate y and solve for x:
15y - 15y = 35 + 3
0 = 38
Since 0 does not equal 38, this system of equations has no solution.
In conclusion, equating coefficients is a fundamental condition in the elimination method as it simplifies the process of solving systems of linear equations and leads to accurate results.
Elimination method in solving systems of linear equations involves eliminating one variable by adding or subtracting the equations. In order to successfully apply this method, it is crucial to equate either of the coefficients. Here's why:
Why equating coefficients is important:
- When we equate the coefficients of either x or y in the two equations, we can easily eliminate one variable by adding or subtracting the equations.
- This ensures that the resulting equation after elimination will have only one variable, making it easier to solve for that variable.
- Equating coefficients helps simplify the process of solving the system of equations and reduces the chances of making errors.
Example:
Let's consider the following system of equations:
2x + 3y = 7
4x - 5y = 1
To eliminate y, we need to equate the coefficients of y in the two equations. In this case, we can multiply the first equation by 5 and the second equation by 3 to get:
15y = 35
-15y = 3
By adding these two equations, we eliminate y and solve for x:
15y - 15y = 35 + 3
0 = 38
Since 0 does not equal 38, this system of equations has no solution.
In conclusion, equating coefficients is a fundamental condition in the elimination method as it simplifies the process of solving systems of linear equations and leads to accurate results.
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Community Answer
In elimination method _____________ is an important condition.a...
In the elimination method we equate either of the coefficient so that the other is eliminated ,substituting the value of one variable into the other equation and then we are left with the linear equation which is solvable and values of the variables are obtained.
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In elimination method _____________ is an important condition.a)Equating either of the coefficientsb)Equating only the y coefficient.c)Equating only the x co-efficient.d)Equating both the coefficients.Correct answer is option 'A'. Can you explain this answer?
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