Respuesta :

texaschic101
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:

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

Step-by-step explanation:

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

[tex]a_1x+b_1y=c_1[/tex]..[1]

[tex]a_2x+b_2y=c_2[/tex]..[2]

[tex]\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}=k[/tex]

So we have ';

4x - Ay = 15..[1]

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

[tex]k=\frac{a_1}{a_2}=\frac{4}{-4}=-1[/tex]

[tex]k=\frac{b_1}{b_2}[/tex]

[tex]-1=\frac{-A}{6}[/tex]

A = 6

[tex]k=\frac{c_1}{c_2}[/tex]

[tex]-1=\frac{15}{B}[/tex]

B = -15

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

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

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

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