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What values of [tex]\( x \)[/tex] and [tex]\( y \)[/tex] satisfy the system of equations [tex]\(\begin{cases}y = 3x + 2 \\ y = 3x - 6\end{cases}\)[/tex]?

Enter your answer as an ordered pair, like this: [tex]\((42, 53)\)[/tex].

If your answer includes one or more fractions, use the / symbol to separate numerators and denominators. For example, [tex]\( \left( \frac{3}{4}, 1 \right) \)[/tex].

If there is no solution, enter "no"; if there are infinitely many solutions, enter "inf."

[tex]\[ \boxed{\phantom{answer}} \][/tex]

Sagot :

GinnyAnsweridn
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]
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