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Sagot :
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]
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]
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