Question

$51x + 12y = 75 \\ 12x + 51y = 114$
what is x and y

Answer 1

X=1, y=2
First add and then subtract.

Answer 2

Hey friend, Harish Here.

Here is your answer.
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$51x +12y = 75$  - (i)

$12x+51y=114$  - (ii)

Now, add equation (i) and (ii).

=> $51x+12x +51y+12y = 75+114$

=>$63x+63y=189$

=>$63(x+y)=189$

=>$x+y = \frac{189}{63}$

=>$x+y = 3$

=>[tex]x=(3-y) [/tex] - (iii)

Now, Substitute (iii) equation (the x value) in (i) or (ii).

Let us substitute the x value in (i) .

=>$51x+12y=75$

=>$51(3-y)+12y=75$

=>$153-51y+12y=75$

=>$153-75=51y-12y$

=>$78 = 39y$

=>$y= \frac{78}{39}$

∴ $y=2$

Now, Substitute y value in equation (iii).

=>$x=3-y$

=>$x=3-2$

∴$x=1$


So, the value of x = 1 & y = 2.
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Hope my answer is helpful to u.