What is the solution to the system of equations: 2x + y = 10 and x - y = 1?

• A. (2, 3)
• B. (3, 4)
• C. (4, 5)
• D. (5, 6)

Answer: (B)

To find the solution to the system of equations given by (2x + y = 10) and (x - y = 1), we can solve this system using the method of substitution or elimination.

First, let's rearrange the second equation, (x - y = 1), to express (y) in terms of (x):

[

y = x - 1

]

Next, we substitute this expression for (y) back into the first equation:

[

2x + (x - 1) = 10

]

Now, simplify the equation:

[

2x + x - 1 = 10

]

[

3x - 1 = 10

]

Adding 1 to both sides gives:

[

3x = 11

]

Now, dividing both sides by 3 yields:

[

x = \frac{11}{3}

]

Next, we substitute (x) back into the expression for (y):

[

y = \frac{11}{3} - 1 = \frac{11}{3} - \frac{3}{3} = \frac{8}{3}