If x.[(2,3)] + y.[(-1,1)] = [(10,5)] , find the values of x and y.

Question

If x.\( \begin{bmatrix} 2 \\[0.3em] 3 \\[0.3em] \end{bmatrix}\) + y.\( \begin{bmatrix} -1 \\[0.3em] 1 \\[0.3em] \end{bmatrix}\) = \( \begin{bmatrix} 10 \\[0.3em] 5 \\[0.3em] \end{bmatrix},\) find the values of x and y.

x.[(2,3)] + y.[(-1,1)] = [(10,5)]

Answer 1

And we have,

\( \begin{bmatrix} 2x - y \\[0.3em] 3x + y \\[0.3em] \end{bmatrix}\) = \( \begin{bmatrix} 10 \\[0.3em] 5\\[0.3em] \end{bmatrix}\) 

Solving the linear equations, we get,

x = 3, y = -4