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Simplifying (x + -1y)(xr + -1xs + -1ys + yt) = (x + y)(p + -1q) Multiply (x + -1y) * (rx + -1sx + -1sy + ty) (x(rx + -1sx + -1sy + ty) + -1y * (rx + -1sx + -1sy + ty)) = (x + y)(p + -1q) ((rx * x + -1sx * x + -1sy * x + ty * x) + -1y * (rx + -1sx + -1sy + ty)) = (x + y)(p + -1q) Reorder the terms: ((rx2 + -1sxy + -1sx2 + txy) + -1y * (rx + -1sx + -1sy + ty)) = (x + y)(p + -1q) ((rx2 + -1sxy + -1sx2 + txy) + -1y * (rx + -1sx + -1sy + ty)) = (x + y)(p + -1q) (rx2 + -1sxy + -1sx2 + txy + (rx * -1y + -1sx * -1y + -1sy * -1y + ty * -1y)) = (x + y)(p + -1q) (rx2 + -1sxy + -1sx2 + txy + (-1rxy + 1sxy + 1sy2 + -1ty2)) = (x + y)(p + -1q) Reorder the terms: (-1rxy + rx2 + -1sxy + 1sxy + -1sx2 + 1sy2 + txy + -1ty2) = (x + y)(p + -1q) Combine like terms: -1sxy + 1sxy = 0 (-1rxy + rx2 + 0 + -1sx2 + 1sy2 + txy + -1ty2) = (x + y)(p + -1q) (-1rxy + rx2 + -1sx2 + 1sy2 + txy + -1ty2) = (x + y)(p + -1q) Multiply (x + y) * (p + -1q) -1rxy + rx2 + -1sx2 + 1sy2 + txy + -1ty2 = (x(p + -1q) + y(p + -1q)) -1rxy + rx2 + -1sx2 + 1sy2 + txy + -1ty2 = ((p * x + -1q * x) + y(p + -1q)) -1rxy + rx2 + -1sx2 + 1sy2 + txy + -1ty2 = ((px + -1qx) + y(p + -1q)) -1rxy + rx2 + -1sx2 + 1sy2 + txy + -1ty2 = (px + -1qx + (p * y + -1q * y)) -1rxy + rx2 + -1sx2 + 1sy2 + txy + -1ty2 = (px + -1qx + (py + -1qy)) Reorder the terms: -1rxy + rx2 + -1sx2 + 1sy2 + txy + -1ty2 = (px + py + -1qx + -1qy) -1rxy + rx2 + -1sx2 + 1sy2 + txy + -1ty2 = (px + py + -1qx + -1qy) Solving -1rxy + rx2 + -1sx2 + 1sy2 + txy + -1ty2 = px + py + -1qx + -1qy Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add 'sx2' to each side of the equation. -1rxy + rx2 + -1sx2 + 1sy2 + txy + sx2 + -1ty2 = px + py + -1qx + -1qy + sx2 Reorder the terms: -1rxy + rx2 + -1sx2 + sx2 + 1sy2 + txy + -1ty2 = px + py + -1qx + -1qy + sx2 Combine like terms: -1sx2 + sx2 = 0 -1rxy + rx2 + 0 + 1sy2 + txy + -1ty2 = px + py + -1qx + -1qy + sx2 -1rxy + rx2 + 1sy2 + txy + -1ty2 = px + py + -1qx + -1qy + sx2 Add '-1sy2' to each side of the equation. -1rxy + rx2 + 1sy2 + txy + -1sy2 + -1ty2 = px + py + -1qx + -1qy + sx2 + -1sy2 Reorder the terms: -1rxy + rx2 + 1sy2 + -1sy2 + txy + -1ty2 = px + py + -1qx + -1qy + sx2 + -1sy2 Combine like terms: 1sy2 + -1sy2 = 0 -1rxy + rx2 + 0 + txy + -1ty2 = px + py + -1qx + -1qy + sx2 + -1sy2 -1rxy + rx2 + txy + -1ty2 = px + py + -1qx + -1qy + sx2 + -1sy2 Add '-1txy' to each side of the equation. -1rxy + rx2 + txy + -1txy + -1ty2 = px + py + -1qx + -1qy + sx2 + -1sy2 + -1txy Combine like terms: txy + -1txy = 0 -1rxy + rx2 + 0 + -1ty2 = px + py + -1qx + -1qy + sx2 + -1sy2 + -1txy -1rxy + rx2 + -1ty2 = px + py + -1qx + -1qy + sx2 + -1sy2 + -1txy Add 'ty2' to each side of the equation. -1rxy + rx2 + -1ty2 + ty2 = px + py + -1qx + -1qy + sx2 + -1sy2 + -1txy + ty2 Combine like terms: -1ty2 + ty2 = 0 -1rxy + rx2 + 0 = px + py + -1qx + -1qy + sx2 + -1sy2 + -1txy + ty2 -1rxy + rx2 = px + py + -1qx + -1qy + sx2 + -1sy2 + -1txy + ty2 Reorder the terms: -1px + -1py + qx + qy + -1rxy + rx2 + -1sx2 + sy2 + txy + -1ty2 = px + py + -1qx + -1qy + sx2 + -1sy2 + -1txy + ty2 + -1px + -1py + qx + qy + -1sx2 + sy2 + txy + -1ty2 Reorder the terms: -1px + -1py + qx + qy + -1rxy + rx2 + -1sx2 + sy2 + txy + -1ty2 = px + -1px + py + -1py + -1qx + qx + -1qy + qy + sx2 + -1sx2 + -1sy2 + sy2 + -1txy + txy + ty2 + -1ty2 Combine like terms: px + -1px = 0 -1px + -1py + qx + qy + -1rxy + rx2 + -1sx2 + sy2 + txy + -1ty2 = 0 + py + -1py + -1qx + qx + -1qy + qy + sx2 + -1sx2 + -1sy2 + sy2 + -1txy + txy + ty2 + -1ty2 -1px + -1py + qx + qy + -1rxy + rx2 + -1sx2 + sy2 + txy + -1ty2 = py + -1py + -1qx + qx + -1qy + qy + sx2 + -1sx2 + -1sy2 + sy2 + -1txy + txy + ty2 + -1ty2 Combine like terms: py + -1py = 0 -1px + -1py + qx + qy + -1rxy + rx2 + -1sx2 + sy2 + txy + -1ty2 = 0 + -1qx + qx + -1qy + qy + sx2 + -1sx2 + -1sy2 + sy2 + -1txy + txy + ty2 + -1ty2 -1px + -1py + qx + qy + -1rxy + rx2 + -1sx2 + sy2 + txy + -1ty2 = -1qx + qx + -1qy + qy + sx2 + -1sx2 + -1sy2 + sy2 + -1txy + txy + ty2 + -1ty2 Combine like terms: -1qx + qx = 0 -1px + -1py + qx + qy + -1rxy + rx2 + -1sx2 + sy2 + txy + -1ty2 = 0 + -1qy + qy + sx2 + -1sx2 + -1sy2 + sy2 + -1txy + txy + ty2 + -1ty2 -1px + -1py + qx + qy + -1rxy + rx2 + -1sx2 + sy2 + txy + -1ty2 = -1qy + qy + sx2 + -1sx2 + -1sy2 + sy2 + -1txy + txy + ty2 + -1ty2 Combine like terms: -1qy + qy = 0 -1px + -1py + qx + qy + -1rxy + rx2 + -1sx2 + sy2 + txy + -1ty2 = 0 + sx2 + -1sx2 + -1sy2 + sy2 + -1txy + txy + ty2 + -1ty2 -1px + -1py + qx + qy + -1rxy + rx2 + -1sx2 + sy2 + txy + -1ty2 = sx2 + -1sx2 + -1sy2 + sy2 + -1txy + txy + ty2 + -1ty2 Combine like terms: sx2 + -1sx2 = 0 -1px + -1py + qx + qy + -1rxy + rx2 + -1sx2 + sy2 + txy + -1ty2 = 0 + -1sy2 + sy2 + -1txy + txy + ty2 + -1ty2 -1px + -1py + qx + qy + -1rxy + rx2 + -1sx2 + sy2 + txy + -1ty2 = -1sy2 + sy2 + -1txy + txy + ty2 + -1ty2 Combine like terms: -1sy2 + sy2 = 0 -1px + -1py + qx + qy + -1rxy + rx2 + -1sx2 + sy2 + txy + -1ty2 = 0 + -1txy + txy + ty2 + -1ty2 -1px + -1py + qx + qy + -1rxy + rx2 + -1sx2 + sy2 + txy + -1ty2 = -1txy + txy + ty2 + -1ty2 Combine like terms: -1txy + txy = 0 -1px + -1py + qx + qy + -1rxy + rx2 + -1sx2 + sy2 + txy + -1ty2 = 0 + ty2 + -1ty2 -1px + -1py + qx + qy + -1rxy + rx2 + -1sx2 + sy2 + txy + -1ty2 = ty2 + -1ty2 Combine like terms: ty2 + -1ty2 = 0 -1px + -1py + qx + qy + -1rxy + rx2 + -1sx2 + sy2 + txy + -1ty2 = 0 The solution to this equation could not be determined.
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