Writing a System of Equations

At the end of the 2000 WNBA regular season, the Houston comets had 22 more victories than losses. The number of victories they had was three less than six time the number of losses. How many regular season games did the Houston comets play during the 2000 WNBA season?



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Dec 17, 2010
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by: Karin

To solve this problem, you must write a system of equations. A system of equations is two equations that satisfy the problem and can then be solved using one of three methods.

Since all of the information revolves around the number of losses we will let x = the number of losses and v = the number of victories.

To write our first equation, we know that the number of victories is 22 more than the number of losses, so our first equation is:

v = x + 22

For our second equation, we know that the number of victories is also 3 less than 6 times the number of losses, so our second equation is:

v = 6x - 3

Now, we have two equations:

v = x +22
v = 6x -3

You can either use graphing, substitution, or linear combinations (addition) to solve this system of equations. I am going to use the substitution method.

We will substitute the expression in equation #2 for v into equation #1.

6x - 3 = x + 22

Now we can solve for x.

Step 1: Subtract x from both sides.

6x - x - 3 = x -x + 22

5x -3 = 22

Step 2: Add three to both sides.

5x - 3 + 3 = 22 + 3
5x = 25

Step 3: Divide both sides by 5

5x/5 = 25/5

x = 5

The number of losses = 5.

Now substitute 5 into one of the equations to find out the number of victories.

x + 22 = v
5 + 22 = 27

Therefore, there were 27 victories.

The question asks for the number of games played, so 5 losses plus 27 victories is equal to 32 games played.


I hope this helps,
Karin

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