Login/Sign Up
Find the value of x if \[\left[ \begin{align} & 3x+y\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,-y \\ & 2y-x\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,3 \\ \end{align} \right]=\left[ \begin{align} & 1\,\,\,\,\,2 \\ & -5\,\,\,3 \\ \end{align} \right]\]
Find the value of x if \[\left[ \begin{align} & 3x+y\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,-y \\ & 2y-x\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,3 \\ \end{align} \right]=\left[ \begin{align} & 1\,\,\,\,\,2 \\ & -5\,\,\,3 \\ \end{align} \right]\]
Class 10 | Exercise 1 | ICSE | Maths | Matrices | ML Aggarwal
Find the value of x if \[\left[ \begin{align} & 3x+y\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,-y \\ & 2y-x\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,3 \\ \end{align} \right]=\left[ \begin{align} & 1\,\,\,\,\,2 \\ & -5\,\,\,3 \\ \end{align} \right]\]

Given

\[\left[ \begin{align}

& 3x+y\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,-y \\

& 2y-x\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,3 \\

\end{align} \right]=\left[ \begin{align}

& 1\,\,\,\,\,2 \\

& -5\,\,\,3 \\

\end{align} \right]\]

Comparing the corresponding terms of given matrix we get

\[-y\text{ }=\text{ }2\]

Therefore \[y=-2\]

Again we have

\[\begin{array}{*{35}{l}}

3x\text{ }+\text{ }y\text{ }=\text{ }1  \\

3x\text{ }=\text{ }1\text{ }\text{ }y  \\

\end{array}\]

Substituting the value of y we get

\[\begin{array}{*{35}{l}}

3x\text{ }=\text{ }1\text{ }\text{ }\left( -2 \right)  \\

3x\text{ }=\text{ }1\text{ }+\text{ }2  \\

3x\text{ }=\text{ }3  \\

x\text{ }=\text{ }3/3  \\

x\text{ }=\text{ }1  \\

\end{array}\]

Hence \[x\text{ }=\text{ }1\text{ }and\text{ }y\text{ }=\text{ }-2\]

i

More Material