The given equations are
12x + 4y = 152 ...........1
32x + 12y = 420 .....2
Multiplying equation 1 by 3 to make coefficient of y same we have:
36x+12y= 456
32x+12y=420
Subtracting the two equations we have:
4x=36.
Dividing by 4 both sides
x= 9.
Substituting x value in equation 1
12(9) + 4y = 152
108+4y=152
Subtracting 108 both sides: 4y=44.
Dividing both sides by 4.
y=11.
cost of the vegetarian lunch is $11.
In the equations, x represents the cost of a chicken lunch and y represents the cost of a vegetarian lunch.