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Find the value of [tex]$Q$[/tex] in the following system so that the solution to the system is [tex]$\{(x, y): x - 3y = 4\}$[/tex].

[tex]\[
\begin{array}{l}
x - 3y = 4 \\
2x - 6y = Q
\end{array}
\][/tex]

Answer here: ________

Sagot :

GinnyAnswer
To find the value of [tex]\( Q \)[/tex] in the given system of equations, we need to analyze the equations provided:

1. [tex]\( x - 3y = 4 \)[/tex]
2. [tex]\( 2x - 6y = Q \)[/tex]

Notice that the second equation, [tex]\( 2x - 6y = Q \)[/tex], appears to be a multiple of the first equation, [tex]\( x - 3y = 4 \)[/tex]. Specifically, if we multiply the first equation by 2, we would get:

[tex]\[ 2(x - 3y) = 2 \cdot 4 \][/tex]

Simplifying the left side of the equation:

[tex]\[ 2x - 6y = 8 \][/tex]

This equation matches the form of the second equation given in our system. Therefore, we can deduce that [tex]\( Q = 8 \)[/tex].

So, the value of [tex]\( Q \)[/tex] so that the solution to the system remains consistent with [tex]\( x - 3y = 4 \)[/tex] is [tex]\( 8 \)[/tex]:

[tex]\[ Q = 8 \][/tex]
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