Question

Got a fairly simple looking system of equations, 2k+4y=20, and 3x+6y=30 Don't understand how to prove what values of k provide - 1 solution - no solutions - and many solutions

Answer 1

2kx+4y=20 ⇒ kx+2y=10

3x+6y=30 ⇒ x+2y= 10

k is the coefficient of x, so it is the slope of the line

• when k=1, both equations will be same, then there are many solutions
• when k=0 there is one solution
• when k is anything different, then the lines will be parallel, so no solutions