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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 :

GinnyAnsweridn
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]
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