Answer:
1.) a = -1/10, b = -8
2.) a =10 , b =0
Step-by-step explanation:
1.) In order for a system of equations to have one solution, the equation must not be parallel or the same equation. Other than that, there are no other restrictions. In order to find what A cannot equal, you must distribute the first equation, 2(5x - 4). B can be equal to anything as long as A is not the same.
2(5x - 4) = (2*5x) + (2*-4) = 10x - 8
10x - 8 = Ax + B
Basically, like I said above, for it to have one solution, A cannot equal 10 or the equation would have no solution or infinite solutions.
For simplistic reasons, I will make A perpendicular to 10x and B will stay the same.
The perpendicular slope of 10 is -1/10, because the reciprocal of 10/1 (just flipping over the number) is 1/10 and the opposite sign of + is -.
So, a possible value for A and B are:
A = -1/10
B = -8
2.) For a system to have no solutions, the equations must be parallel to each other; in order to be parallel, the slopes must be the same and the y-intercepts (b) must NOT be the same.
Since 10x - 8 = Ax + B
A must = 10
B cannot = -8, but can be any other number so let's make B = 0 just because.
So a possible value for A and B are:
A = 10
B = 0
