SOLUTION: 3x+4y=62 & 5x+2y=52

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Question 1107608: 3x+4y=62 & 5x+2y=52
Found 2 solutions by addingup, ikleyn:
Answer by addingup(3677)   (Show Source): You can put this solution on YOUR website!
3x+4y=62 & 5x+2y=52
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5x+2y=52: multiply all times -2 and add to the other equation
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3x+4y=62
+
-10x-4y= -104
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-7x 0y = -42
-7x = - 42
x = -42/-7 divide to get your answer. Remember that -/- = + so in this case you can ignore the - sign, just divide 42/7 or do it in your head, by now you should know that 42 is the product of 7 x 6
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Now find y, substitute in the original equations:
3x+4y=62; 3(6)+4y = 62; 18+4y = 62; 4y = 44; y = 11
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Check: let's try the answers in the two equations:
3x+4y=62; 3(6)+4(11) = 62; 18+44 = 62 Correct
Now the other equation:
5x+2y=52; 5(6)+2(11) = 52; 30+22 = 52 Also correct.
You now have the correct answers.
Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.
 3x + 4y = 62,      (1)
 5x + 2y = 52.      (2)


To solve the system, I will use the Elimination method. For it, multiply the equation (2) by 2 (both sides).
Keep equation (1) unchanged. You will get

 3x + 4y =  62,     (1')
10x + 4y = 104.     (2')


Now subtract equation (1') from equation {2'). The terms "4y", that are equal in both equations
(that I made equal in both equations) will cancel each other, and you will get a single equation containing only one unknown "x"

10x - 3x = 104 - 62,   or

7x = 42.


It is how the Elimination method works.

Now   x =  = 6.


So, you just found the value of x= 6.
Now substitute this value into either of the two given/original equations and find y.   I will use equation (1):

3*6 + 4y = 62  ====>  4y = 62 - 3*6 = 44  ====>  y =  = 11.


Answer.  x= 6,  y= 11.


Check.   Check the solution on your own.



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