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
Δ=∣2−312∣=4+3=7\Delta = \left| {\begin{matrix} 2&{ - 3}\\ 1&2 \end{matrix}} \right| = 4 + 3 = 7Δ=∣∣21−32∣∣=4+3=7
Δ1=∣K−3−22∣=2K−6{\Delta _1} = \left| {\begin{matrix} K&{ - 3}\\ { - 2}&2 \end{matrix}} \right| = 2K - 6Δ1=∣∣K−2−32∣∣=2K−6
Δ2=∣2K1−2∣=−4−K{\Delta _2} = \left| {\begin{matrix} 2&K\\ 1&{ - 2} \end{matrix}} \right| = - 4 - KΔ2=∣∣21K−2∣∣=−4−K
Then
x=Δ1Δ=2K−67x = \frac{{{\Delta _1}}}{\Delta } = \frac{{2K - 6}}{7}x=ΔΔ1=72K−6
y=Δ2Δ=−4−K7y = \frac{{{\Delta _2}}}{\Delta } = \frac{{ - 4 - K}}{7}y=ΔΔ2=7−4−K
Answer: x=2K−67,y=−4−K7x = \frac{{2K - 6}}{7}, y = \frac{{ - 4 - K}}{7}x=72K−6,y=7−4−K
Need a fast expert's response?
and get a quick answer at the best price
for any assignment or question with DETAILED EXPLANATIONS!
Comments