Question

To solve the system of linear equations 3 x minus 2 y = 4 and 9 x minus 6 y = 12 by using the linear combination method, Henry decided that he should first multiply the first equation by –3 and then add the two equations together to eliminate the x-terms. When he did so, he also eliminated the y-terms and got the equation 0 = 0, so he thought that the system of equations must have an infinite number of solutions. To check his answer, he graphed the equations 3 x minus 2 y = 4 and 9 x minus 6 y = 12 with his graphing calculator, but he could only see one line. Why is this?

(20pt)
because the system of equations actually has only one solution
because the system of equations actually has no solution
because the graphs of the two equations overlap each other
because the graph of one of the equations does not exist

Answer 1

"because the graphs of the two equations overlap each other"

Explanation:

If he graphs both equations on the graphing calculator and it shows only one line this can mean only one thing:

Both linear equations are the same

An example of this is

x+y=2

2x+2x=4

If you simplify the second equation by dividing everything by 2 you get the same equation as the first one

This means the answer would be "because the graphs of the two equations overlap each other"