Question

Which values for A and B will create infinitely many solutions for this system of equations? Ax-y=8 2x+y=B plss hurry im being timed

1 A=2 B=8
2 A=-2 B=8
3 A=2 B=-8
4 A=-2 B=-8

Answer 1

A=-2

B=-8

Explanation:

In order for the system of linear equations to have infinitely many solution, they must be the same equation.

Ax-y=8

2x+y=B

We need to choose A and B so they are the same equation.

I notice they are both in the same form but in the second column you have opposites;

the -y and y.

So im going to multiply either equation by -1 so that part is exactly the same.

Don't choose both; choose only one.

Let's multiply the first equation by -1.

Doing this gives us the following:

-Ax+y=-8

2x+y=B

So now we can choose A and B so these equations appear exactly the same.

We need -A=2 and B=-8.

-A=2 implies A=(opposite of 2) which is -2.

Conclusion:

A=-2

B=-8

Answer 2

A = -2 and B = -8.

Explanation:

Two lines
`a_1x+b_1y+c_1=0\text{ and }a_2x+b_2y+c_2=0` have infinite many solutions if

`(a_1)/(a_2)=(b_1)/(b_2)=(c_1)/(c_2)`

The given equations are

`Ax-y=8`

`2x-y=B`

These equations have infinite many solutions if

`(A)/(2)=(-1)/(1)=(8)/(B)`

`(A)/(2)=-1=(8)/(B)`

`(A)/(2)=-1` or
`-1=(8)/(B)`

`A=-2` or
`-B=8\Rightarrow B=-8`

Hence, the value of A is -2 and the value of B is -8.