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Class 9 Tuition > Learn Mathematics > Solve : 55x + 52y = 217; 52x + 55y = 217
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Solve : 55x + 52y = 217; 52x + 55y = 217

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subtract two equations from each other, we get x=y and then substitute x=y in any of the equation we get values for x and y . x=1.972 ,y= 1.972
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Firstly, from the first equation, find x. From eqn 1: x = 217 - 52y/55. Now, substitute this value of x in the first eqn. i.e. 52 X (217 - 52y)/55 = 217 Now, multiply both sides with the denominator 55. Therefore, the eqn is 52(217-52y) + 3025y=11935 Solve for y. y = 217/107 ...
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Firstly, from the first equation, find x. From eqn 1: x = 217 - 52y/55. Now, substitute this value of x in the first eqn. i.e. 52 X (217 - 52y)/55 = 217 Now, multiply both sides with the denominator 55. Therefore, the eqn is 52(217-52y) + 3025y=11935 Solve for y. y = 217/107 Now, substitute this value of y in the x = 217 - 52y/55 which was derived from the original eqn. Therefore x = 217 - 52(217/107) /55 which is x = 217/107. Therefore, x = y = 217/107 read less
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First of all this is a question of simultaneous equations. But it has a trick under its sleeve. The main thing is to identify that little twist in this question. The RHS of both the equations have the same number. So, if we subtract one equation from the other, we can express x in terms of y. Lets...
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First of all this is a question of simultaneous equations. But it has a trick under its sleeve. The main thing is to identify that little twist in this question. The RHS of both the equations have the same number. So, if we subtract one equation from the other, we can express x in terms of y. Lets do it... 55x + 52y - 52x - 55y = 217-217 3x - 3y = 0 x = y. Great!! We got x = y. So substituting x in place of y in 1st equation we can get the value of x. Therefore, 55x + 52x = 217 107x = 217 x = 217/107 = 2.028 Also, y = x So y = 2.028 Therefore, the solution is (2.028,2.028) read less
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X=Y=217/107
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Trainer

=>55x+52y=217..........................(i) =>52x+55y=217..........................(ii) Adding equation (i) & (ii), We have 77 (x+y)=434 =>x+y=434/77..................(iii) Subtracting (ii) from (i), We have=>x-y=0-----------------------(iv) From equation (iii) & (iv), we have x=217/77 y=217...
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As the summation of both eqns are same, we can equate the equations 52x+55y = 55x+52y => 3y=3x ( same eqn can be achieved by subtracting both eqns) => x=y Now putting this in any eqn We get 55x + 52x=217 => 107x=217 => x =y=217/107
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Eco, Maths and Stats Tutor

subtract any one of the equations from another to get x=y. substitute this in any one of the equations to get x=y=2.03
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