If x + 3y = 8 and 4x – 7y = 1, what is the value of x + y?  

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We have the two equations x + 3y = 8 and 4x – 7y = 1. We can see that it is not possible to multiply the equations by any number and add or subtract them to achieve a common coefficient for x and y that can be canceled to yield the value of x+y.

So, let’s find x and y and use that to determine their sum.

We have x + 3y = 8

=> x = 8 – 3y

substitute this in 4x – 7y = 1

=> 4(8 – 3y) – 7y = 1

=> 32 – 12y – 7y = 1

=> -19y = -31

=> y = 31/19

x = 8 – 3*(31/19)

=> x = 59/19

The sum x + y = 31/19 + 59/19 = 90/19

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