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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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
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.
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