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.

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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

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