The problem consists of two parts. Part 1: Solve the following system of linear equations: $x - y = 20$ $x + y = 130$ Part 2: Hamza paid 130 Dh for vegetables and fruits. The price of the vegetables is 20 Dh more than the price of the fruits. Determine the price paid for the vegetables and the price paid for the fruits.

1. Problem Description

The problem consists of two parts.

Part 1: Solve the following system of linear equations:

$x - y = 20$

$x + y = 130$

Part 2: Hamza paid 130 Dh for vegetables and fruits. The price of the vegetables is 20 Dh more than the price of the fruits. Determine the price paid for the vegetables and the price paid for the fruits.

2. Solution Steps

Part 1:

We have the system of equations:

$x - y = 20$ (1)

$x + y = 130$ (2)

Adding equations (1) and (2), we get:

$(x - y) + (x + y) = 20 + 130$

$2x = 150$

$x = \frac{150}{2}$

$x = 75$

Substituting $x = 75$ into equation (2), we get:

$75 + y = 130$

$y = 130 - 75$

$y = 55$

So the solution to the system is $x = 75$ and $y = 55$.

Part 2:

Let $l$ be the price of the vegetables and $f$ be the price of the fruits.

We are given that the total price is 130 Dh, so:

$l + f = 130$ (3)

We are also given that the price of the vegetables is 20 Dh more than the price of the fruits, so:

$l = f + 20$ (4)

Substitute equation (4) into equation (3):

$(f + 20) + f = 130$

$2f + 20 = 130$

$2f = 130 - 20$

$2f = 110$

$f = \frac{110}{2}$

$f = 55$

Now, substitute $f = 55$ into equation (4):

$l = 55 + 20$

$l = 75$

Therefore, the price of the vegetables is 75 Dh and the price of the fruits is 55 Dh.

3. Final Answer

Part 1: The solution to the system of equations is $x = 75$ and $y = 55$.

Part 2: The price paid for the vegetables is 75 Dh and the price paid for the fruits is 55 Dh.