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

-9x + 3y = -42...divide by -3
3x - y = 14...same as first equation....means same line...means infinite solutions

answer is : 3rd answer choice

Answer 2

Answer:

The answer is C

$3x-y=14\\-9x+3y=-42$

Step-by-step explanation:

In order to determine the system, we have to know the condition to produce infinitely solutions. A solution of a system is the coordinate (x,y) which is common between two lines ( in a 2D plane). A system does not have solution when the lines do not intercept each other, that it means, they are parallele. When two lines are coincident in all points, there are infinitely solutions.

I have attached an image that shows different systems of two lines.

So, to find the system, we have to find two equal equation. If we multiply by 3 the third system:

$3x-y=14\\-9x+3y=-42\\\\(-3)*(3x-y)=(-3)*14\\(1)*(-9x+3y)=(1)*-42\\\\-9x+3y=-42\\-9x+3y=-42$

This system has infinitely solutions.