How do you determine whether a linear system has one solution, many solutions, or no solution when given 8x - 7y = -3 and 6x - 5y = -1?

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Answer 1 · 2018-03-05T12:27:17

Has one solution, #x=4 , y=5#

Let linear system of equation are #a_1x+b_1y=c_1# and

#a_2x+b_2y=c_2# .If #a_1/a_2=b_1/b_2 =c_1/c_2# there is

infinite number of solutions. The lines will overlap. If

#a_1/a_2=b_1/b_2 # , then there is no solution . The lines are

parallal. If #a_1/a_2 !=b_1/b_2 # , then there is one solution .

#8x-7y=-3 (1) # and #6x-5y=-1 (2) # Here

#8/6 != (-7)/-5# , so there is one solution.

Solution: #24x-21y=-9 (3) # and #24x-20y=-4 (2) #

Subtracting (3) from (4) we get #y=5 :. x= (-1+5*5)/6=4#

So has one solution, #x=4 , y=5# [Ans]