The equation to represent the area of the triangle would be: y = 1/2(x²) - (7/2)x The equation to represent the perimeter of the triangle would be: y = 3x - 6 The solutions to the system would be (12, 30) or (1, -3). The only viable solution is (12, 30).Explanation The area of a triangle is found using the formula A = 1/2bh For our triangle, b = x and h = x-7, so we have: A = 1/2(x)(x-7) A = 1/2(x²-7x) A = 1/2(x²) - (7/2)x We will replace A with y, so we have: y = 1/2(x²) - (7/2)x The perimeter of a triangle is found by adding together all sides, so we have: P = (x-7) + x + (x+1) Combining like terms we get: P = 3x - 6 We will replace P with y, so we have: y = 3x - 6 Since both equations have y isolated on one side, it will be easy to use substitution to solve the system: 3x - 6 = 1/2(x²) - (7/2)x It's easier to work with whole numbers, so we will multiply everything by 2: 6x - 12 = x² - 7x We want all of the variables on one side, so we will subtract 6x: 6x - 12 - 6x = x² - 7x - 6x -12 = x² - 13x When solving quadratics, we want the equation equal to 0, so we will add 12: -12+12 = x² - 13x + 12 0 = x² - 13x + 12 This is easy to factor, as there are factors of 12 that sum to -13; -12(-1) = 12 and -12+-1 = -13: 0 = (x-12)(x-1) Using the zero product property, we know that either x-12=0 or x-1=0; therefore x=12 or x=1. Putting these back into our equation for perimeter (the simplest one) we have: y = 3(12)-6 = 36-6 = 30; (12, 30); y = 3(1) - 6 = 3 - 6 = -3; (1, -3) We cannot have a negative perimeter, so the only viable solution is (12, 30).