Question #208637

Solve the simultaneous equation +=5 and +=1


1
Expert's answer
2021-06-22T08:49:00-0400

a1x+b1y=5a2x+b2y=1a1a2x+b1a2y=5a2a1a2x+a1b2y=a1(b1a2a1b2)y=5a2a1y=5a2a1b1a2a1b2a1b2x+b1b2y=5b2b1a2x+b1b2y=b1(a1b2b1a2)x=5b2b1x=5b2b1a1b2b1a2\displaystyle a_1x + b_1y = 5\\ a_2x + b_2y = 1\\ a_1a_2x + b_1a_2y = 5a_2\\ a_1a_2x + a_1b_2y = a_1\\ (b_1a_2 - a_1b_2)y = 5a_2 - a_1\\ y = \frac{5a_2 - a_1}{b_1a_2 - a_1b_2}\\ a_1b_2x + b_1b_2y = 5b_2\\ b_1a_2x + b_1b_2y = b_1\\ (a_1b_2 - b_1a_2)x = 5b_2 - b_1\\ x = \frac{5b_2 - b_1}{a_1b_2 - b_1a_2}\\


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