Writing and Solving Systems of Equations

by Chuck

The sum of Eli's age and Cecil's age is 60. Six years ago, Eli was three times as old as Cecil.Find Eli's age now.

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Writing and Solving Systems of Equations

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Feb 22, 2012
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starstarstarstarstar 		Writing and Solving Systems of Equations NEW
by: Karin

For this problem, you already have one equation solved for one variable: a = 4b

Step 1: Substitute 4b for a into the 2nd equation.

3(4b) - 2b =30
12b -2b =30
10b = 30
10b/10 = 30/10
b = 3

Step 2: Substitute 3 for b into the equation:
a = 4b
a = 4(3)
a = 12

Solution: a = 12 and b = 3
Feb 22, 2012
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starstarstarstarstar 		please solve this NEW
by: Anonymous

please solve this:

a=4b---->E1
3a-2b=30----->E2
Dec 08, 2010
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starstarstarstarstar 		Writing and Solving a System of Equations
by: Karin

In order to solve this problem, you must write a system of equations.

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,
Karin

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