Given the equation 4x-3y=7, write a second linear equation to create a system that:

has exactly one solution.

has no solution.

has infinitely many solutions.

One way is to solve for y first

4x-3y=7
minus 4
-3y=-4x+7
divide by -3
y=4/3x+7/3
y=mx+b
m=sloope
b=yintercept
ok, so with 1 solution is different slope and differetn y int
y=3x+9 would be first

no solution means same slopt with different y int so they are paralell
y=4/3x+9

infinite solutions means same line, but disguised
2y=8/3x-14/3 (just multiply everybody by 2)

so
1 solution: 3x-4y=7
no solution: 4x-3y=anynumberexcept7 so 4x-3y=9
infinite solutions simplifies to 4x-3y=7, example 8x-6y=14