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?

i have a time limit someone answer fast plsss (taking this down at 4:20 pm)

Answer 1

• 3x-2y=4
• 9x-6y=12

Divide second equation by 3

• 3x-2y=4

LInes are same so you can see only one line

Answer 2

The lines are:

• 3x - 2y = 4

and

• 9x - 6y = 12

Since after multiplying by -3 the equations sum to 0, the equations are same.

Same equations produce overlapping lines, hence you can see one line only.