What are the values of \(x\) and \(y\) in the system of equations \(2x + 3y = 6\) and \(x - y = 1\)?

To find the values of (x) and (y) in the system of equations given by (2x + 3y = 6) and (x - y = 1), we can use substitution or elimination.

First, let's solve the second equation for (x):

[

x = y + 1

]

Now, we can substitute (x) in the first equation:

[

2(y + 1) + 3y = 6.

]

Distributing gives:

[

2y + 2 + 3y = 6.

]

Combining like terms results in:

[

5y + 2 = 6.

]

Subtracting 2 from both sides yields:

[

5y = 4,

]

and then dividing by 5 gives:

[

y = \frac{4}{5}.

]

Now, substitute (y = \frac{4}{5}) back into the expression we found for (x):

[

x = \frac{4}{5} + 1 = \frac{4}{5} + \frac{5}{5} = \frac{9}{5}.

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