To solve for [tex]\( x \)[/tex] and [tex]\( y \)[/tex] in the given system of equations and then find the value of [tex]\( x + 4 \)[/tex], we follow these steps:
We start with the system of linear equations:
[tex]\[
2x + 17y = 63 \quad \text{(1)}
\][/tex]
[tex]\[
17x + 28y = 62 \quad \text{(2)}
\][/tex]
First, we need to solve the system to find the values of [tex]\( x \)[/tex] and [tex]\( y \)[/tex].
Through solving the system of equations simultaneously, we get:
[tex]\[
x = -\frac{710}{233}
\][/tex]
[tex]\[
y = \frac{947}{233}
\][/tex]
Next, we are required to find the value of [tex]\( x + 4 \)[/tex].
Now, we substitute the value of [tex]\( x \)[/tex] into the expression [tex]\( x + 4 \)[/tex]:
[tex]\[
x + 4 = -\frac{710}{233} + 4
\][/tex]
To simplify this expression, we get a common denominator for the fractions:
[tex]\[
4 = \frac{4 \times 233}{233} = \frac{932}{233}
\][/tex]
So,
[tex]\[
x + 4 = -\frac{710}{233} + \frac{932}{233}
\][/tex]
[tex]\[
x + 4 = \frac{-710 + 932}{233}
\][/tex]
[tex]\[
x + 4 = \frac{222}{233}
\][/tex]
Therefore, the value of [tex]\( x + 4 \)[/tex] is:
[tex]\[
\boxed{\frac{222}{233}}
\][/tex]
Thus, the detailed steps lead us to conclude that [tex]\( x + 4 = \frac{222}{233} \)[/tex].
