Question

Solve the following system of equations:

2x+3y = 11
4x-2y=6
1. x=2 y=3
2. x=1 y=4
3. x=3 y=1
4. x=4 y=2

Answer 1

Upon solving the given system of equations, the values of x and y were found to be x = 2.5 and y = 2, which does not match any of the provided options. There may be a typo or incorrect information given in the question.

Step-by-step explanation:

To solve the following system of equations:

• 2x+3y = 11
• 4x-2y=6

We will solve the simultaneous equations for x and y.

1. First, we'll multiply the first equation by 2, so that we can eliminate y by adding it to the second equation:
   2*(2x+3y) = 2*11 which gives 4x+6y = 22.
2. Adding the second original equation, 4x-2y=6, to the modified first equation, we get:
   (4x+6y) + (4x-2y) = 22+6, which simplifies to:
   8x+4y = 28.
3. Now divide the resulting equation by 4, we get:
   2x+y = 7.
4. Next, we'll subtract the first original equation from this result to solve for y:
   (2x+y) - (2x+3y) = 7-11, which simplifies to:
   -2y = -4...
5. From the last result, we find that y = 2.
6. Substituting y = 2 into the first original equation, 2x+3y = 11 gives us:
   2x + 3*(2) = 11,
   which simplifies to:
   2x + 6 = 11, and finally
   x = 2.5, which is not an option given.

It seems there has been a mistake because none of the provided options matches our calculations. The correct values of x and y should be rechecked. Please ensure there are no typos in the options provided or the system of equations.