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Q: What is the percentage proportion of these taxes in relation to your income andwith respect to your disposable income (that is income after taxes)?
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Is the simultaneous equation x2 plus y2 equals 25 y equals x plus 1 even possible?

Yes, it's possible(1) x2 + y2 = 25(2) y = x + 1Substituting (2) into (1) gives:(3) x2 + (x + 1)2 = 25(4) x2 + x2 + 2x + 1 = 25(5) 2x2 + 2x - 24 = 0(6) x2 + x - 12 = 0Plugging 1, 1, and -12 into the quadratic equation gives us two answers:x = 3, y - 4 and x = -4, y = -3==================================================Another contributor was working this at exactly the same time as the firstcontributor, and posts his work here, just to demonstrate how great mindsrun in the same gutter:Shouldn't be a big problem. When you think about this for a while, it might seem like it might not be very difficult; but then, when you dig into it a little further, it turns out to be downright easy.The first glance:x2+y2=25 is a circle, centered at the origin, with radius=25.y=x+1 is a 45-degree line, shifted one unit above the origin.They have two common points ... the two points where the 45-degree line cutsthe circle. Those two points are the solutions to the simultaneous equations.Since they're on a circle, we can't tell right away where the points will be, andwith fear and trembling, we hesitantly write them down and try to solve themalgebraically.The drudge work:Substitute [y=x+1] into [x2 + y2 = 25]:x 2 + (x+1)2 = 25x2 + x2 + 2x + 1 = 252x2 + 2x -24 = 0x2 + x - 12 = 0We don't even need to resort to the quadratic formula to solve this! We canjust look at it and factor it:(x-4)(x+3) = 0x = 4, (y = -3)x = -3, (y = 4)Well, you and I can factor it just by looking at it, but the middle-schooler whose homework we're doing probably needs to show his (our) work.