Question

Determine which system below will produce infinitely many solutions. −6x + 3y = 18 4x − 3y = 6 2x + 4y = 24 6x + 12y = 36 3x − y = 14 −9x + 3y = −42 5x + 2y = 13 −x + 4y = −6

Answer 1

3x - y = 14.....multiply by 3
-9x + 3y = -42
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9x - 3y = 42 (result of multiplying by 3)
-9x + 3y = -42
-----------------add
0 = 0 (correct...infinitely many solutions)

Answer 2

Answer:

Option C is correct.

System of equation which will produce infinitely many solutions:

3x - y = 14        

-9x +3y = -42  

Step-by-step explanation:

From the options

Only equation which is infinitely many solutions is

3x - y = 14                ......[1]

-9x +3y = -42           ......[2]

For infinitely many solutions, we are looking for linearly dependent equations, which means one equation is an exact multiple or sub-multiple of the other.

Multiply [1] by -3 we get

$-3(3x-y) = -3\cdot 14$

or

-9x + 3y = -42 which is same equation as [2]

therefore. by definition of infinitely many solution,

equation 2 is -3 times(or multiple) of equation 1