Respuesta :
Answer:
A=-2
B=-8
Step-by-step 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:
A = -2 and B = -8.
Step-by-step explanation:
Two lines [tex]a_1x+b_1y+c_1=0\text{ and }a_2x+b_2y+c_2=0[/tex] have infinite many solutions if
[tex]\dfrac{a_1}{a_2}=\dfrac{b_1}{b_2}=\dfrac{c_1}{c_2}[/tex]
The given equations are
[tex]Ax-y=8[/tex]
[tex]2x-y=B[/tex]
These equations have infinite many solutions if
[tex]\dfrac{A}{2}=\dfrac{-1}{1}=\dfrac{8}{B}[/tex]
[tex]\dfrac{A}{2}=-1=\dfrac{8}{B}[/tex]
[tex]\dfrac{A}{2}=-1[/tex] or [tex]-1=\dfrac{8}{B}[/tex]
[tex]A=-2[/tex] or [tex]-B=8\Rightarrow B=-8[/tex]
Hence, the value of A is -2 and the value of B is -8.
