The problem involves solving the system of equations provided to find the prices of a banana and a sandwich. Let us denote:

• $x$: the price of a banana (in kr)
• $y$: the price of a sandwich (in kr)

The equations are:

$4x + y = 38$ $3x + 2y = 46$

Step 1: Solve for $y$ in terms of $x$ from the first equation:

$y = 38 - 4x$

Step 2: Substitute $y = 38 - 4x$ into the second equation:

$3x + 2(38 - 4x) = 46$ Expand and simplify: $3x + 76 - 8x = 46$ $-5x + 76 = 46$ $-5x = -30$ $x = 6$

Step 3: Substitute $x = 6$ into $y = 38 - 4x$:

$y = 38 - 4(6)$ $y = 38 - 24$ $y = 14$

Final Results:

• The price of a banana ($x$) is 6 kr.
• The price of a sandwich ($y$) is 14 kr.

Would you like more detailed steps or additional explanations? Let me know!

Here are 5 follow-up questions:

1. How would the results change if the price of four bananas and a sandwich was increased to 50 kr?
2. Can you write the problem as a matrix equation and solve it using matrix methods?
3. How would you solve this system graphically?
4. Can you verify the solution by substituting $x = 6$ and $y = 14$ back into both equations?
5. What happens to the system if the coefficients of $x$ and $y$ in the second equation are doubled?

Tip: To verify your results, substitute the values back into the original equations to ensure they hold true.