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?

1 Answer
Mar 5, 2018

Has one solution, x=4 , y=5

Explanation:

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]