To determine which of the listed pairs [tex]\((x, y)\)[/tex] is a solution to the equation [tex]\( 3x - y = 5 \)[/tex], we will substitute each pair into the equation and verify if it holds true.
Let's evaluate each option step by step:
### Option (a): [tex]\( x = 0, y = 5 \)[/tex]
Substitute [tex]\( x = 0 \)[/tex] and [tex]\( y = 5 \)[/tex] into the equation [tex]\( 3x - y = 5 \)[/tex]:
[tex]\[ 3(0) - 5 = 0 - 5 = -5 \][/tex]
The left side of the equation equals [tex]\(-5\)[/tex], which does not equal the right side, [tex]\( 5 \)[/tex]. So, [tex]\( (0, 5) \)[/tex] is not a solution.
### Option (b): [tex]\( x = 5, y = 0 \)[/tex]
Substitute [tex]\( x = 5 \)[/tex] and [tex]\( y = 0 \)[/tex] into the equation [tex]\( 3x - y = 5 \)[/tex]:
[tex]\[ 3(5) - 0 = 15 - 0 = 15 \][/tex]
The left side of the equation equals [tex]\(15\)[/tex], which does not equal the right side, [tex]\( 5 \)[/tex]. So, [tex]\( (5, 0) \)[/tex] is not a solution.
### Option (c): [tex]\( x = -5, y = 0 \)[/tex]
Substitute [tex]\( x = -5 \)[/tex] and [tex]\( y = 0 \)[/tex] into the equation [tex]\( 3x - y = 5 \)[/tex]:
[tex]\[ 3(-5) - 0 = -15 - 0 = -15 \][/tex]
The left side of the equation equals [tex]\(-15\)[/tex], which does not equal the right side, [tex]\( 5 \)[/tex]. So, [tex]\( (-5, 0) \)[/tex] is not a solution.
### Option (d): [tex]\( x = 0, y = -5 \)[/tex]
Substitute [tex]\( x = 0 \)[/tex] and [tex]\( y = -5 \)[/tex] into the equation [tex]\( 3x - y = 5 \)[/tex]:
[tex]\[ 3(0) - (-5) = 0 + 5 = 5 \][/tex]
The left side of the equation equals [tex]\( 5 \)[/tex], which matches the right side, [tex]\( 5 \)[/tex]. So, [tex]\( (0, -5) \)[/tex] is a solution.
Therefore, the correct answer is:
[tex]\[
\text{d) } x = 0, y = -5
\][/tex]
