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Introduction |
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we often study more than one equations in the same two variables at the same time. The equations under consideration are said to form "simultaneous equations". We shall study in this chapter, a pair of linear equations in two variables, and methods of finding solutions common to both the equations. |
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Simultaneous Equation |
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Solving two equations simultaneously means to find the common solution of both the equations, i.e., a solution which satisfies both the equations. (Such a common solution, if it exists, can be shown to be unique.)
The following two methods are used to find a solution:
(a) Method of elimination
(b) Method of substitution. |
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Method of Elimination (by Addition) |
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Solve the Systems of Linear Equations by Method of Elimination (by Addition): 3x - 4y = 20 …(i)
5x + 6y = 8 …(ii). |
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Substitution Method |
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Solve the Systems of Linear Equations by Method of Substitution: 2x - 9y = 0 …(i)
x - 18y = 27 … (ii). |
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Problems on Simultaneous Equations |
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Solve the following Systems of Linear Equations:
1.If one number is thrice the other and their sum is 60, find the numbers.
2.Find the fraction which becomes 1/2 when the denominator is increased by 5 and is equal to 1/3 when the numerator is diminished by 4.
3.Six years hence a man's age will be three times his son's age, and three years ago he was nine times as old as his son. Find their present ages.
4.The sum of the digits of a two digit number is 7. If the digits are reversed, the new number increased by 3 equals four times the original number. Find the original number.
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Summary |
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Finding the solution by the method of substitution.
(i) Coefficients of one of the variables (say x) in the two equations are made equal, by multiplying them with suitable factors.
(ii) By addition or subtraction, this variable (x) is eliminated.
(iii) The value of the other variable (y) is obtained and by substitution we obtain x.
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