Question

A linear system of two equations is shown y=4x+6 y=4x-5 How many solutions does the system have?

Answer 1

This system has no solutions because it possible can't be true that y = 4x + 6 and y is also equal to 4x - 5.

y = 4x + 6
y = 4x - 5

These two can't be true for any value of x.

Answer 2

two linear system always have one intersection unless they are parallel

Answer 3

In which case, they have "no solution".

Answer 4

if the lines are parallel, then 2 conditions can occur. No solutions and infinite solutions. In this case, they have the same slope by differ by a constant; so they cross the y axis at different points; hence, no solution.

Answer 5

Correct. I missed that case.