Explanation:
The first equation is pretty easy to write.
The sum of Eli and Cecil's age is 60.
Let x = Eli's age
Let y = Cecil's age
Sum means add, so:
x + y = 60
The second equation is a little tricker.
Six years ago, Eli was three times as old as Cecil.
Six years ago means we have to subtract 6
Think:
Eli (six years ago) = 3 times cecil's age (six years ago)
x - 6 = 3(y-6)
Now, let's use the distributive property.
x - 6 = 3y - 18
Next we'll get the variables on one side and the constants on the other in order to write the equation in standard form.
x - 3y - 6 = 3y -3y - 18 Subtract 3y
x - 3y - 6 = -18
x - 3y - 6 + 6 = -18 + 6 Add 6
x - 3y = -12
Now we have two equation in standard form:
x + y = 60
x - 3y = -12
You can solve easily by using substitution or linear combinations.
I will use the linear combinations method.
Step 1: Create 1 set of opposite terms.
x + y = 60
-1 ( x - 3y) = -12(-1)
x + y = 60
-x + 3y = 12
Step 2: Add
x + y = 60
-x + 3y =12
--------------
4y = 72
Step 3: Solve for y
4y/4 = 72/4
y = 18
Cecil's age is 18
Step 4: Substitute to find Eli's age.
x + y = 60
x + 18 = 60
x+18 - 18 = 60 -18
x = 42
Eli's age is 42.
Check:
42 + 18 = 60
Six years ago:
Eli was 36
Cecil was 12
Eli was 3 times as old as Cecil 6 years ago.
12 * 3 = 36
Hope this helps