Let h = hot dog
Let s = soft drink
4h + s = 6.30...Equation A
h + 4s = 4.20...Equation B
We have two equations in two unknowns. The unknowns are the variables h and s.
I will solve for s in Equation A by subtracting 4h from both sides.
s = -4h + 6.30
I will now replace s in Equation B with -4h + 6.30 to find the price of one hot dog.
h + 4(-4h + 6.30) = 4.20
h -16h + 25.2 = 4.20
-15h = -25.2 + 4.20
-15h = -21
Divide both sides by -15.
h = -21/-15
h = 21/15
h = 7/5
h = $1.40
We now know the value of one hot dog.
Go back to EITHER Equation A or B, replace h with 1.40, do the algebra and you will find the price of one soft drink.