Question

PLEASEEEE
Which of the following systems of equations has infinitely many solutions?
3x - 3y = 11; 6y = 9x - 22
5y = -9x - 6; -27x + 15y = 15
4x - 7y = 7; -14y = 8x - 14
-4x + 2 = 3y; 12y - 8 = -16x

Answer 1

The last option because the first and second equations are the same.
To be able to see that, rearrange the second one like this: -16x+8=12y
then divide through by 4 to get : -4x+2=3y

Answer 2

good question!
so let me try
if the determinant of a system is zero then the system have infinite many solution
let me solve first one i hope you can do the rest
first of all the equations must be standard form
ax+by=c form
we have
3x - 3y = 11; .............1

6y = 9x - 22 ................2
write the second equation in standard form
9x-6y=22
so we have two equations in standard form
3x - 3y = 11;
9x-6y = 22;
write in matrix form
\[\Large A=\left[\begin{matrix}3 & -3 \\ 9 & -6\end{matrix}\right]\]
now taking determinant
\[\Large \det(A)=(3)(-6)-(9)(-3)=9\]
since
\[\Large \det(A)\neq0\]
so the system does not have infinite many solutions!

can you check the rest in the same way???

Answer 3

so its the last one?

Answer 4

@mc32141 check the determinant of the last one if it is zero then yes it is !

Answer 5

@sami-21 Hadn't thought about it that way. nice. :) And yes, @mc32141 you should get the determinant as zero.

Answer 6

@allank i think it is easy way :) because if the two rows in determinant will gets similar then it will be zero.

Answer 7

@mc32141 did you get it?