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Solve the system of equations \begin{aligned} &2 x+5 y=1\\ &3 x+2 y=7 \end{aligned}  Speed
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09:04 ## QuestionMathsClass 12

Solve the system of equations \begin{aligned} &2 x+5 y=1\\ &3 x+2 y=7 \end{aligned}

The system of equations can be written in the form AX = B, where
A = $$\left[\begin{array}{ll} {2} & {5} \\ {3} & {2} \end{array}\right], X=\left[\begin{array}{l} {x} \\ {y} \end{array}\right]$$ and B = $$\left[\begin{array}{l} {1} \\ {7} \end{array}\right]$$
Now, A = –11 $$\neq$$ 0, Hence, A is nonsingular matrix and so has a unique solution.
Note that $$A^{-1}=-\frac{1}{11}\left[\begin{array}{cc} {2} & {-5} \\ {-3} & {2} \end{array}\right]$$
Therefore X = A–1B = –$$\frac{1}{11}\left[\begin{array}{cc} {2} & {-5} \\ {-3} & {2} \end{array}\right]\left[\begin{array}{l} {1} \\ {7} \end{array}\right]$$
i.e., $$\left[\begin{array}{l} {x} \\ {y} \end{array}\right]=-\frac{1}{11}\left[\begin{array}{c} {-33} \\ {11} \end{array}\right]=\left[\begin{array}{c} {3} \\ {-1} \end{array}\right]$$
Hence, x = 3, y = – 1          