The unknown values are:
- number of calories in a slice of bread
- number of calories in an egg
We can use letters b and e to name these two variables (that way it is easier to remember which one represents what, b for bread and e for egg).
b = number of calories in a slice of bread
e = number of calories in an egg
Translate the relevant information into algebraic statements:
1st sentence: 2b + 3e = 357
2nd sentence: b + 2e = 217
3rd sentence: b = ?, e = ?
Solve the system:
2b + 3e = 357
b + 2e = 217
Multiply the second equation by (-2) and add the resulting equation to the first one.
The intention here is to eliminate variable b (because it is easier than to eliminate variable e) and reduce the system from 2 equations with 2 unknowns down to 1 equation with 1 unknown.
(b + 2e = 217) * (-2)
----------------------
-2b - 4e = -434
2b + 3e = 357
-2b - 4e = -434
----------------------
- e = - 77
Solve the above equation by multiplying it by (-1)
(- e = - 77) * (-1)
----------------------
e = 77
Solved for e. Now solve for b by using the obtained value for e.
For this purpose, we can use any of the two original equations.
Let's take the second one since it will be easier to solve for e.
b + 2e = 217
b + 2(77) = 217
b + 154 = 217
b = 63
Solved.
Number of calories in a slice of bread is 63.
Number of calories in an egg is 77.