Question 576079
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Row 2 has the values 0 -3 -6 -24, which means that -3y -6z = -24. Solve for y to get


-3y -6z = -24


-3y = 6z -24


y = (6z)/(-3) -24/(-3)


y = -2z + 8


Now if you let z = P (ie let z be the free variable), then y = -2P + 8. So that explains why the second coordinate is -2P+8 and the third is P



Now that you know that z = P and y = -2P+8, you can use this to find x in terms of the free variable P (or z). So use the first equation (you can use any equation that has x in it)



x + 3y +5z = 20


x + 3(-2P+8) +5P = 20


x -6P+24 +5P = 20


x -P+24 = 20


x -P = 20-24


x -P = -4


x = P-4


So the solutions are


x = P-4, y = -2P+8, and z = P


which form the ordered triple


(P-4, -2P+8, P)