# Answer to Question #3632 in Algebra for murni

Question #3632

Find all pairs of value of x and y such that

(3x+y+1)/8 = (x-y)/5 = (x

(3x+y+1)/8 = (x-y)/5 = (x

^{2}-y^{2})/5Expert's answer

These equation can be rewritten in such form:(3x+y+1)/8 = (x-y)/5 AND (x - y) / 5 = (x

After substituting into the second equation, we have:

x + (7x + 5) / -7 = x

x

1) x = (19 + √(553)) / 24 AND y = (7*(19 + √(553)) / 24 + 5) / -7

2) y = (19 - √(553)) / 24 AND y = (7*(19 - √(553)) / 24 + 5) / -7

^{2}- y^{2}) / 5From the first equation: y = (7x + 5) / -7After substituting into the second equation, we have:

x + (7x + 5) / -7 = x

^{2}- ((7x + 5) / -7)^{2}12x^{2}- 19x - 4 = 0D = 361 + 192 = 553x

_{1}= (19 + √(553)) / 24, x_{2}= (19 - sqrt(553)) / 24so, we have such pairs:1) x = (19 + √(553)) / 24 AND y = (7*(19 + √(553)) / 24 + 5) / -7

2) y = (19 - √(553)) / 24 AND y = (7*(19 - √(553)) / 24 + 5) / -7

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