# Solve the simultaneous equations, 5x + 2y = 20 , x + 4y= 13

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(Equation 1) 5x + 2y = 20  (Equation 2) x + 4y= 13

As we know the values for x and y are the same in both equations, we can use them to find out the values for both, In order to do this we need to take one equation and define it by either x or y, for example taking equation 2 and definining x in terms of y by rearranging the equation.

x + 4y = 13

x= 13 - 4y

Now we have x defined in terms of y we can put this into equation 1 and simplify to get a value for y.

5x + 2y = 20

5(13-4y) + 2y = 20

65 - 20y +2y = 20

65 - 18y = 20

-18y = -45

18y = 45

y = 2.5

Now that we have a value for y we can use that for find x. If we put our value for y into equation 2

x + 4y = 13

x + 4(2.5) = 13

x + 10 = 13

x = 3

Now we have our two values for x and y we have solved the simultaneous equations, to check they're correct we should substitute both values into either equation and see if the equation is correct.

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