tell whether the system has one solution , infinitely many solutions,or no solution

Question

y=1/2x+3

2y-x=6

Answer 1

Greetings! Lets solve this shall we ?

So, we must find out if there are infinitely many solutions, no solution, or one solution. Then, we must modify one of the equations into slope-intercept form such that,

2y - x = 6...............Add x to the other side such that

2y = x + 6..............Then divide 2 to both sides such that

y = (1/2)x + 3

Notice this equation is the same as the other y = (1/2)x + 3. Therefore, the system has infinitely many solutions!

I hope this helped!