Answer :
To find the values of [tex]\( x \)[/tex] and [tex]\( y \)[/tex] that satisfy the system of equations
[tex]\[ \begin{cases} y = 3x + 2 \\ y = 3x - 6 \end{cases} \][/tex]
follow these steps:
1. Since both equations equal [tex]\( y \)[/tex], we set the two right-hand sides equal to each other:
[tex]\[ 3x + 2 = 3x - 6 \][/tex]
2. Subtract [tex]\( 3x \)[/tex] from both sides to eliminate [tex]\( x \)[/tex]:
[tex]\[ 2 = -6 \][/tex]
3. The resulting equation [tex]\( 2 = -6 \)[/tex] is a contradiction, which means there are no values of [tex]\( x \)[/tex] that satisfy both equations simultaneously. Therefore, the system of equations has no solution.
So the correct answer is:
[tex]\[ \boxed{\text{no}} \][/tex]
[tex]\[ \begin{cases} y = 3x + 2 \\ y = 3x - 6 \end{cases} \][/tex]
follow these steps:
1. Since both equations equal [tex]\( y \)[/tex], we set the two right-hand sides equal to each other:
[tex]\[ 3x + 2 = 3x - 6 \][/tex]
2. Subtract [tex]\( 3x \)[/tex] from both sides to eliminate [tex]\( x \)[/tex]:
[tex]\[ 2 = -6 \][/tex]
3. The resulting equation [tex]\( 2 = -6 \)[/tex] is a contradiction, which means there are no values of [tex]\( x \)[/tex] that satisfy both equations simultaneously. Therefore, the system of equations has no solution.
So the correct answer is:
[tex]\[ \boxed{\text{no}} \][/tex]