Muhammad Ortiz

Mathematics

8 September, 21:53

To solve the system of linear equations 3x - 2y - 4 and 9x-by = 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 3x-2y = 4 and 9x-by = 12 with his graphing calculator,

but he could only see one line. Why is this?

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