Question

Pls solve this simultaneous equation using elimination method.

Six pencils and three rubbers cost N1170. Five pencils and two rubbers cost N920. How much does each cost?

Answer 1

To solve the simultaneous equations using the elimination method, we need to set up the equations based on the information given.

Let:
- \(x\) = cost of one pencil
- \(y\) = cost of one rubber

From the problems stated, we can create the following equations:

1) From the first statement:
\[ 6x + 3y = 1170 \]
2) From the second statement:
\[ 5x + 2y = 920 \]

Now, we have the system of equations:
\[
\begin{align*}
6x + 3y &= 1170 \quad \text{(1)} \\
5x + 2y &= 920 \quad \text{(2)}
\end{align*}
\]

### Step 1: Simplify Equation (1)

To simplify equation (1), we can divide the entire equation by 3:
\[
2x + y = 390 \quad \text{(3)}
\]

### Step 2: Solve for \(y\) in terms of \(x\) from Equation (3)

Rearranging equation (3):
\[
y = 390 - 2x \quad \text{(4)}
\]

### Step 3: Substitute Equation (4) into Equation (2)

Now, substitute equation (4) into equation (2):
\[
5x + 2(390 - 2x) = 920
\]
Expanding this:
\[
5x + 780 - 4x = 920
\]
Combining like terms:
\[
x + 780 = 920
\]
Subtracting 780 from both sides:
\[
x = 920 - 780
\]
\[
x = 140
\]

### Step 4: Substitute \(x\) back into Equation (4) to find \(y\)

Now substitute \(x = 140\) back into equation (4) to find \(y\):
\[
y = 390 - 2(140)
\]
Calculating this:
\[
y = 390 - 280
\]
\[
y = 110
\]

### Conclusion

The cost of each item is:
- The cost of one pencil (x) = N140
- The cost of one rubber (y) = N110

Thus, the final answer is:
- **Cost of one pencil: N140**
- **Cost of one rubber: N110**