There are 2 equations given and two unknown things in the form of x and y that needs to be found.
15x + 12y = 292.50
15x = 292.50 - 12 y
x = (292.5 - 12y)/15
Now we have to replace the value of x that has been deduced into the second equation.
Then
45x + 10y = 747.50
45[(292.5 - 12y)/15] + 10y = 747.50
3(292.5 - 12y) + 10y = 747.5
877.5 - 36y + 10y = 747.5
-26y = -130
y = 5
Now we will be replacing the value of y in any of the given equations to find the value of x
15x = 12y = 292.5
15x + 12(5) = 292.5
15x + 60 = 292.5
15x = 292.5 - 60
15x = 232.5
x = 232.5/15
= 15.5