Let's determine whether the point [tex]\((3, 5)\)[/tex] is a solution to the given system of linear equations.
Given system:
[tex]\[
\begin{array}{l}
-15x + 7y = 1 \\
3x - y = 1
\end{array}
\][/tex]
### Step 1: Substitute [tex]\((3, 5)\)[/tex] into the first equation
Substitute [tex]\(x = 3\)[/tex] and [tex]\(y = 5\)[/tex] into the first equation:
[tex]\[
-15(3) + 7(5) = 1
\][/tex]
Calculate:
[tex]\[
-45 + 35 = -10
\][/tex]
This gives:
[tex]\[
-10 \neq 1
\][/tex]
So the point [tex]\((3, 5)\)[/tex] does not satisfy the first equation.
### Step 2: Substitute [tex]\((3, 5)\)[/tex] into the second equation
Now, substitute [tex]\(x = 3\)[/tex] and [tex]\(y = 5\)[/tex] into the second equation:
[tex]\[
3(3) - 5 = 1
\][/tex]
Calculate:
[tex]\[
9 - 5 = 4
\][/tex]
This gives:
[tex]\[
4 \neq 1
\][/tex]
So the point [tex]\((3, 5)\)[/tex] also does not satisfy the second equation.
### Conclusion
Since the point [tex]\((3, 5)\)[/tex] does not satisfy either of the equations, it cannot be a solution to the given system of equations.
Thus, the answer is:
[tex]\[
\boxed{\text{False}}
\][/tex]
