To determine the value of [tex]\( k \)[/tex], given that the point [tex]\((1, -1)\)[/tex] is a solution of the equation [tex]\( 3x - ky = 8 \)[/tex], follow these steps:
1. Substitute the given values into the equation:
The point [tex]\((1, -1)\)[/tex] means [tex]\( x = 1 \)[/tex] and [tex]\( y = -1 \)[/tex].
Substitute these values into the equation [tex]\( 3x - ky = 8 \)[/tex]:
[tex]\[
3(1) - k(-1) = 8
\][/tex]
2. Simplify the equation:
Calculate [tex]\( 3(1) \)[/tex]:
[tex]\[
3 \times 1 = 3
\][/tex]
This gives us:
[tex]\[
3 + k = 8
\][/tex]
3. Solve for [tex]\( k \)[/tex]:
To isolate [tex]\( k \)[/tex], subtract 3 from both sides of the equation:
[tex]\[
3 + k - 3 = 8 - 3
\][/tex]
Simplifying the equation:
[tex]\[
k = 5
\][/tex]
Therefore, the value of [tex]\( k \)[/tex] is [tex]\( 5 \)[/tex].
