Solve the equation: [3 2 5 5] [x1 x2]+ [1 2]= [2 -3]

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   Answer:

     (x1, x2) = (3, -4)

   Step-by-step explanation:

   As with any 2-step linear equation, subtract the constant, then multiply by the inverse of the coefficient of the variable.

     [tex]\left[\begin{array}{cc}3&2\\5&5\end{array}\right]\left[\begin{array}{c}x\\y\end{array}\right]+\left[\begin{array}{c}1\\2\end{array}\right]=\left[\begin{array}{c}2\\-3\end{array}\right]\\\\\left[\begin{array}{cc}3&2\\5&5\end{array}\right]\left[\begin{array}{c}x\\y\end{array}\right]=\left[\begin{array}{c}1\\-5\end{array}\right]\\\\\left[\begin{array}{c}x\\y\end{array}\right]=\dfrac{1}{5}\left[\begin{array}{cc}5&-2\\-5&3\end{array}\right]\left[\begin{array}{c}1\\-5\end{array}\right][/tex]

   Performing the multiplication of the matrix by the vector gives the solution.

     x = ((5)(1) +(-2)(-5))/5 = 15/5 = 3

     y = ((-5)(1) +(3)(-5))/5 = -20/5 = -4

   Using your variables, x1, x2, the solution is …

     (x1, x2) = (3, -4)

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