Question #176975

use Cramer's Rule to find the solution of the systems of linear equation in terms of the parameter K.


2x - 3y = K

x + 2y = -2


1
Expert's answer
2021-04-14T13:11:43-0400

Δ=2312=4+3=7\Delta = \left| {\begin{matrix} 2&{ - 3}\\ 1&2 \end{matrix}} \right| = 4 + 3 = 7

Δ1=K322=2K6{\Delta _1} = \left| {\begin{matrix} K&{ - 3}\\ { - 2}&2 \end{matrix}} \right| = 2K - 6

Δ2=2K12=4K{\Delta _2} = \left| {\begin{matrix} 2&K\\ 1&{ - 2} \end{matrix}} \right| = - 4 - K

Then

x=Δ1Δ=2K67x = \frac{{{\Delta _1}}}{\Delta } = \frac{{2K - 6}}{7}

y=Δ2Δ=4K7y = \frac{{{\Delta _2}}}{\Delta } = \frac{{ - 4 - K}}{7}

Answer: x=2K67,y=4K7x = \frac{{2K - 6}}{7}, y = \frac{{ - 4 - K}}{7}


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