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