Question

How do I find out how many solutions does each system of equations have?

Answer 1

To do that you should put it in slope intercept form and then graph, you should already know how to do this.

Answer 2

If they are the exact same equation then there are infinte soltuions
if they have same slope but different y intercept then there are 0 solutions
if different slope then 1 soltuiosn



basically
if ax+by=c and ex+fy=g, when simplified
1. a=e and b=f and c=g, then infinite solutions
2. a=e and b=f and c≠g, then 0 solutions
3. if a≠e or/and b≠f and/or c≠g then 1 solutions
confusing





a.
3x-y=1 and 3y+3=9x
3x-y=1 and 3=9x-3y
3x-y=1 and 9x-3y=3
3x-y=1 and 3x-y=1
same equtions
infinite solutions




b.
y+4x=7 and -2y-4=8x
y+4x=7 and -4=8x+2y
y+4x=7 and 8x+2y=-4
y+4x=7 and 4x+y=-2
y+4x=7 and y+4x=-2
same slope but differen y int
0 solutions




c.
4y=3x+4 and 8y-6x=8
-3x+4y=4 and 8y-6x=8
4y-3x=4 and 8y-6x=8
4y-3x=4 and 4y-3x=4
same
inifninte soltuions