Sure! Let's start by expressing [tex]\( y \)[/tex] in terms of [tex]\( x \)[/tex] in the given equation.
The given equation is:
[tex]\[ 2x - y = 6 \][/tex]
To express [tex]\( y \)[/tex] in terms of [tex]\( x \)[/tex], we need to isolate [tex]\( y \)[/tex] on one side of the equation. Here are the steps:
1. Start with the given equation:
[tex]\[ 2x - y = 6 \][/tex]
2. Subtract [tex]\( 2x \)[/tex] from both sides to isolate the term involving [tex]\( y \)[/tex]:
[tex]\[ -y = 6 - 2x \][/tex]
3. Multiply both sides by [tex]\( -1 \)[/tex] to solve for [tex]\( y \)[/tex]:
[tex]\[ y = 2x - 6 \][/tex]
So, [tex]\( y \)[/tex] in terms of [tex]\( x \)[/tex] is:
[tex]\[ y = 2x - 6 \][/tex]
Next, we need to check if the point [tex]\( (1, 4) \)[/tex] is a solution of the equation [tex]\( 2x - y = 6 \)[/tex]. To do this, we'll substitute [tex]\( x = 1 \)[/tex] and [tex]\( y = 4 \)[/tex] into the equation and see if the equation holds true.
Substitute [tex]\( x = 1 \)[/tex] and [tex]\( y = 4 \)[/tex] into the equation [tex]\( 2x - y = 6 \)[/tex]:
[tex]\[ 2(1) - 4 = 6 \][/tex]
[tex]\[ 2 - 4 = 6 \][/tex]
[tex]\[ -2 = 6 \][/tex]
This is not a true statement. Hence, the point [tex]\( (1, 4) \)[/tex] is not a solution of the equation [tex]\( 2x - y = 6 \)[/tex].
To summarize:
- We expressed [tex]\( y \)[/tex] in terms of [tex]\( x \)[/tex] as [tex]\( y = 2x - 6 \)[/tex].
- The point [tex]\( (1, 4) \)[/tex] is not a solution to the equation [tex]\( 2x - y = 6 \)[/tex].
