How do you solve the following system?

Question

$a_1x_1+a_2x_2+a_3=0$ , $a_4x_1+a_5x_2+a_6=0$

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Answer 1 · 2018-06-21T20:43:34

$(x_1,x_2)=((a_2a_6-a_3a_5)/(a_1a_5-a_2a_4) , (a_3a_4-a_1a_6)/(a_1a_5-a_2a_4))$

Here,

$a_1x_1+a_2x_2=-a_3...to(1),where, a_1,a_2,a_3 inRR$

$a_4x_1+a_5x_2=-a_6...to(2) ,where ,a_4,a_5,a_6 in RR$

$"using "color(blue)"Cramer's Rule"$ $"to solve the system :"$

First we find determinants : $D ,D_x and D_y$

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$"Cramer's Rule :"$

$x_1=(D_x)/D =(a_2a_6-a_3a_5)/(a_1a_5-a_2a_4) ,where, a_1a_5-a_2a_4!=0$

$x_2=(D_y)/D =(a_3a_4-a_1a_6)/(a_1a_5-a_2a_4) , where, a_1a_5-a_2a_4!=0$

Hence, the solution of system is :

$(x_1,x_2)=((a_2a_6-a_3a_5)/(a_1a_5-a_2a_4) , (a_3a_4-a_1a_6)/(a_1a_5-a_2a_4)),$

$where, a_1a_5-a_2a_4!=0$