This is a system of equations. You are supposed to formulate two equations and either use the elimination by addition method to solve or the substitution method to solve.
We have to first name two different variables to represent the two unknow values. We choose a & b.
The first statement says the sum of the two values is 18 so we express that algebraically:
a + b = 18
The difference of those same two values is 8:
a - b = 8
Now that we have our two equations, we can choose either method to solve (either method yields the same answer).
Substitution: Choose either equation and solve for one of the variable in that equation:
(2nd equation, solving for a, so will add b to both sides) a = 8 + b Now, we will substitute this value for
"a variable" into the first equation: (8 + b) + b = 18 Now solve for b.
8 + 2b = 18 (now subtract 8 from both sides)
2b = 10 (now divide each side by 2 to get b by itself)
b = 5 Now we will take the value we found for "b" and substitute it back into the second equation and solve for "a":
a - (5) = 8 (add 5 to both sides)
a = 13
Answers are 13, 5
Elimination by addition method:
Set the equations up so you can add them together, eliminating one of the variables and leaving the other.
a + b = 18
a - b = 8 Adding these two equations together, the "b" term cancels out, leaving just the "a" term:
2a = 26 Now we just divide both sides by 2 to solve for "a"
a = 13 Substituting the "a" value into either equation will give us the "b" value.
(13) + b = 18 (subtract 13 from both sides) or (13) - b = 8 (subtract 13 from both sides)
b = 5 or - b = - 5 (and divide both sides by -1)
Hope this helps!
