Complete the square for x and y.
7x^2 + 3y^2 - 28x - 12y = -19
7x^2 - 28x + 3y^2 - 12y = -19
7(x^2 - 4x) + 3(y^2 - 4y) = -19
7(x^2 - 4x + 4) + 3(y^2 - 4y + 4) = -19 + 28 + 12
7(x - 2)^2 + 3(y - 2)^2 = 21
Divide 4.10 by 7 to get about 0.59 (round up because you can't get part of a penny) and that gives you 1/8 of a yard's price. Then multiply that by 8 to get a full yard for $4.72.
Step-by-step explanation:
{2,3,5,7,9,11,13,15,17,19}