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

justaguide | College Teacher | (Level 2) Distinguished Educator

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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

amyhan | Student, Grade 9 | eNotes Newbie

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x+3y = 8 times 4 in both sides

4(x+3y) = 4*8 --> 4x + 12y = 32

then minute 4x-7y = 1

19y = 31 --> y = 31/19

then from x = 8-3y = 8-3*31/19 =59/19

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

neela | High School Teacher | (Level 3) Valedictorian

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Given x+3y = 8....(1) and 4x-7y = 1.....(2). We have to find x+y.

7*(1)+3*(2) eliminates y:

7(x+3y)+3(4x-7y) = 7*8+3*1 = 59.

7x+12x = 59

19x = 59

x = 59/19.

4*(1)- (2) eliminatores x:

4(x+3y)-(4z-7y) = 4*8-1 = 31.

12x+7y = 31.

19y = 31.

y = 31/19.

Therefore x+y = 59/19+31/19 = 90/19.