Question
If $\left[\begin{array}{cc}5 & 2 \\ -1 & y+1\end{array}\right]-2\left[\begin{array}{cc}1 & 2 x-1 \\ 3 & -2\end{array}\right]=\left[\begin{array}{cc}3 & -8 \\ -7 & 2\end{array}\right]$ Find the values of $x$ and $y$
✓
Answer
$
\begin{aligned}
& {\left[\begin{array}{cc}
5 & 2 \\
-1 & y+1
\end{array}\right]-2\left[\begin{array}{cc}
1 & 2 x-1 \\
3 & -2
\end{array}\right]=\left[\begin{array}{cc}
3 & -8 \\
-7 & 2
\end{array}\right]} \\
& \Rightarrow\left[\begin{array}{cc}
5 & 2 \\
-1 & y+1
\end{array}\right]-\left[\begin{array}{cc}
2 & 4 x-2 \\
6 & -4
\end{array}\right]=\left[\begin{array}{cc}
3 & -8 \\
-7 & 2
\end{array}\right] \\
& \Rightarrow\left[\begin{array}{cc}
5-2 & 2-4 x+2 \\
-1-6 & y+1+4
\end{array}\right]=\left[\begin{array}{cc}
3 & -8 \\
-7 & 2
\end{array}\right] \\
& \Rightarrow\left[\begin{array}{cc}
3 & 4-4 x \\
-7 & y+5
\end{array}\right]=\left[\begin{array}{cc}
3 & -8 \\
-7 & 2
\end{array}\right]
\end{aligned}
$
Comparing the corresponding terms, we get
$
\begin{aligned}
& 4-4 x =-8 \\
& \Rightarrow-4 x =-8-4 \\
& \Rightarrow-4 x =-12 \\
& \Rightarrow x =\frac{-12}{-4}=3
\end{aligned}
$
and
$
\begin{aligned}
& y+5=2 \\
& \Rightarrow y=2-5=-3 \\
& \therefore x=3, y=-3 .
\end{aligned}
$
\begin{aligned}
& {\left[\begin{array}{cc}
5 & 2 \\
-1 & y+1
\end{array}\right]-2\left[\begin{array}{cc}
1 & 2 x-1 \\
3 & -2
\end{array}\right]=\left[\begin{array}{cc}
3 & -8 \\
-7 & 2
\end{array}\right]} \\
& \Rightarrow\left[\begin{array}{cc}
5 & 2 \\
-1 & y+1
\end{array}\right]-\left[\begin{array}{cc}
2 & 4 x-2 \\
6 & -4
\end{array}\right]=\left[\begin{array}{cc}
3 & -8 \\
-7 & 2
\end{array}\right] \\
& \Rightarrow\left[\begin{array}{cc}
5-2 & 2-4 x+2 \\
-1-6 & y+1+4
\end{array}\right]=\left[\begin{array}{cc}
3 & -8 \\
-7 & 2
\end{array}\right] \\
& \Rightarrow\left[\begin{array}{cc}
3 & 4-4 x \\
-7 & y+5
\end{array}\right]=\left[\begin{array}{cc}
3 & -8 \\
-7 & 2
\end{array}\right]
\end{aligned}
$
Comparing the corresponding terms, we get
$
\begin{aligned}
& 4-4 x =-8 \\
& \Rightarrow-4 x =-8-4 \\
& \Rightarrow-4 x =-12 \\
& \Rightarrow x =\frac{-12}{-4}=3
\end{aligned}
$
and
$
\begin{aligned}
& y+5=2 \\
& \Rightarrow y=2-5=-3 \\
& \therefore x=3, y=-3 .
\end{aligned}
$
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