MathematicsIf x21+y35+−8−11=0 then (x,y)=___

If $x [\begin{array}{l} 2 \\ 1 \end{array}] + y [\begin{array}{l} 3 \\ 5 \end{array}] + [\begin{array}{l} - 8 \\ - 11 \end{array}] = 0$ then $(x, y) =___$

$x [\begin{array}{l} 2 \\ 1 \end{array}] + y [\begin{array}{l} 3 \\ 5 \end{array}] + [\begin{array}{l} - 8 \\ - 11 \end{array}] = 0$

$\Rightarrow [\begin{array}{l} 2 x + 3 y - 8 \\ 1 x + 5 y - 11 \end{array}] = [\begin{array}{l} 0 \\ 0 \end{array}]$

$\Rightarrow 2 x + 3 y = 8$

$x + 5 y = 11$

Solve the above two equations.

$x = 1, y = 2$

$(x, y) = (1, 2)$

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