Lets represent:
x=cost per bowl
y=cost per plate
y=0.5x
Now lets right the equation:
2x+3y=$1421
Substitute the current value for y
2x+3(0.5)=$1421
2x+1.5x=$1421
3.5x=$1421
x=$406
Each cost of bowl is $406, now lets find the cost of each plate
y=0.5x
y=0.5($406)
y=$203
Each cost of plate is $203. Hope this helps =)