Question 2811: Solve the syatem of eqations for x and y using the addition method:
2x-5y=13
5x+3y=17
Answer by sujatha.krishna(11)   (Show Source):
You can put this solution on YOUR website! If we directly add the 2 LHS (left hand sides) and 2 RHS (right hand sides) of these equations as suggested by addition method of solving a system of linear equations, then we cannot arrive at an answer. Why ? Take a look -
2x - 5y = 13
5x + 3y = 17
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7x - 2y = 30
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You still have two unknowns x and y. So the other way to solve this is to multiply the first equation by 3 and the second one by 5 so that we can arrive at a -15y and a +15y and hence y can be eliminated thereby giving the value of x. How does this work, take a look below -
2x - 5y = 13 (multiply this by 3) This gives 6x - 15y = 39
5x +3y = 17 (multiply this by 5) This gives 25x + 15y = 85
6x - 15y = 39
25x + 15y = 85
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31x = 124
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So x = 124/31 = 4
Now to find the value of y, substitue the value of x in any of the equations. Lets use the first one -
2x - 5y = 13
2(4) - 5y = 13
-5y = 13-8 = 5
5y = -5
y = -5/5 = -1
So the system of these 2 equations is (4,-1)
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