In a competition 5 points are awarded for every game won and two points were deducted for each game lost.Abel attempted 20 games and got 79 points.Form two simultaneous equations and determine the games won by Abel using elimination method 

Let's define two variables for the number of games won and lost by Abel:

- Let \( x \) be the number of games Abel won.
- Let \( y \) be the number of games Abel lost.

### Step 1: Form the simultaneous equations

1. **Total number of games played**:
   Abel attempted 20 games in total, so we have the equation:
   \[
   x + y = 20
   \]
   
2. **Points calculation**:
   Abel earned 5 points for each game won and lost 2 points for each game lost. The total number of points Abel scored is 79, so the second equation is:
   \[
   5x - 2y = 79
   \]

Now, we have the system of two equations:
\[
\begin{align*}
1. \quad x + y &= 20 \\
2. \quad 5x - 2y &= 79
\end{align*}
\]

### Step 2: Solve the system using the elimination method

We will first eliminate one variable. From the first equation \( x + y = 20 \), solve for \( y \):

\[
y = 20 - x
\]

### Step 3: Substitute into the second equation

Substitute \( y = 20 - x \) into the second equation \( 5x - 2y = 79 \):

\[
5x - 2(20 - x) = 79
\]

Simplify the equation:

\[
5x - 40 + 2x = 79
\]
\[
7x - 40 = 79
\]

Add 40 to both sides:

\[
7x = 119
\]

Now, solve for \( x \):

\[
x = \frac{119}{7} = 17
\]

### Step 4: Find \( y \)

Using \( x = 17 \) in the equation \( x + y = 20 \):

\[
17 + y = 20
\]
\[
y = 20 - 17 = 3
\]

### Conclusion:

Abel won **17 games** and lost **3 games**.

Would you like a breakdown of any specific step or more details? Here are some follow-up questions:

1. What is the importance of forming two equations in a word problem like this?
2. How does the elimination method compare to substitution?
3. Can simultaneous equations be solved graphically?
4. What are some common real-life situations where simultaneous equations are useful?
5. How does deducting points in a competition affect the final score?

**Tip**: When dealing with word problems, defining variables clearly and breaking the problem into parts can simplify the solution process.

In a competition 5 points are awarded for every game won and two points were deducted for each game lost. Abel attempted 20 games and got 79 points. Form two simultaneous equations and determine the games won by Abel using the elimination method.

Learn how to solve simultaneous equations using the elimination method in this problem where Abel attempted 20 games, earning 5 points for each win and losing 2 points for each loss. This algebra problem is suitable for students in Grades 8-10 and involves key concepts in linear equations.

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