The given equations are really uncomfortable and do not lend themselves to either substitution or elimination without using big numbers.
Let's equate one of the variables: solve for y in each.
23x+31y =1color(white)(xxxxx)and -7x+5y =-2
31y = 1-23xcolor(white)(xxxxxxxxxxxxxx)5y = 7x-2
y = (1-23x)/31color(white)(xxxxxxxxxxxxxxxx)y = (7x-2)/5
Now as y=y, we can equate the right sides of each equation:
(1-23x)/31 = (7x-2)/5" "larr cross multiply
31(7x-2) =5(1-23x)
217x-62 = 5-115x
217x+115x = 5+62
332x = 67
x = 67/332
Now substitute this value for x into either equation above.
y= (7(67/332)-2)/5
y = (469/332 -2)/5
y = -195/332 div 5
y = -cancel195^39/332 xx1/cancel5
y = -39/332
Check by substituting the values for x and y into the the other equation.
23x +31y
23(67/332) +31(-39/332)
=1
The equation checks out.
