To find the value of [tex]\( Q \)[/tex] in the given system of equations:
[tex]\[ \begin{array}{l}
x - 3y = 4 \\
2x - 6y = Q
\end{array} \][/tex]
we need to manipulate the first equation and compare it to the second.
1. Start with the first equation:
[tex]\[ x - 3y = 4 \][/tex]
2. Multiply both sides of this equation by 2 to have a comparable equation to the second one:
[tex]\[ 2(x - 3y) = 2 \cdot 4 \][/tex]
3. This multiplication gives us:
[tex]\[ 2x - 6y = 8 \][/tex]
4. Now we compare the result [tex]\(2x - 6y = 8\)[/tex] with the second given equation [tex]\(2x - 6y = Q\)[/tex].
By comparing these two equations, we immediately see that:
[tex]\[ Q = 8 \][/tex]
So, the value of [tex]\( Q \)[/tex] that ensures the system of equations maintains the same solution is:
[tex]\[ Q = 8 \][/tex]
