Question

Solve for x and y
47x+31y=63
31x+47y=15​

Answer 1

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$47x + 31y = 63$

$31x + 47y = 15$

Add these equations together

$(47x + 31y) + (31x + 47y)= 63 + 15$

$47x +3 1x + 31y + 47y = 78$

$78x + 78y = 78$

$78(x + y) = 78$

$x + y = \frac{78}{78}$

$x + y = 1$

$y = 1 - x$

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Let's get back to the question, see the first equation :

$47x + 31y = 63$

We know that y = 1 - x (proved above)

$47x + 31(1 - x) = 63$

$47x + 31 - 31x = 63$

$47x - 31x = 63 - 31$

$16x = 32$

$x = 2$

$y = 1 - x = 1 - 2 = - 1$