Question

Which values for A and B will create infinitely many solutions for this system of equations?

4x-AY=15 help me plz so confused!
-4x+6y=B

Answer 1

infinite solutions means that u are dealing with the same line....

4x - 6y = 15
-4x + 6y = -15
--------------------add...as u can see, everything cancels
0 = 0......when u have variables that cancel, leaving u with a true statement, this means there is infinite solutions

Answer 2

The values of A and B are -6 and -15 respectively.

Explanation:

For values for A and B which will create infinitely many solutions for this system of equations. the equation must follow this scheme ;

`a_1x+b_1y=c_1`..[1]

`a_2x+b_2y=c_2`..[2]

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

So we have ';

4x - Ay = 15..[1]

-4x + 6y = B..[2]

`k=(a_1)/(a_2)=(4)/(-4)=-1`

`k=(b_1)/(b_2)`

`-1=(-A)/(6)`

A = 6

`k=(c_1)/(c_2)`

`-1=(15)/(B)`

B = -15

So, the values of A and B are 6 and -15 respectively.

4x - 6y = 15..[1]

-4x + 6y = -15..[2]