Giuliana has 22 quarters and dollar coins worth a total of $10.75

Quarter is $0.25
Dollar is just $1
x is amount of quarters
y is amount of dollar coins
Two equations we know
0.25x+1y=10.75 and
x+y=22

solve both for y
0.25x+1y=10.75
y=10.75-0.25x

x+y=22
y=22-x

set them equal
22-x= (y) =10.75-0.25x
11.25=0.75x
x=15 quarters

then put x=15 into either equation and now solve for y

x+y=22
15+y=22
y=7 dollar coins