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1) isolate x for -x-5y-5z=2: x = -2 - 5y - 5z

substitute x = -2 -5y - 5z

{4(-2 - 5y - 5z) - 5y + 4z = 19}

{-2 - 5y - 5z + 5y - z = -20}

simplify

{-25y - 16z - 8 = 19}

{-6z - 2 = -20}

isolate z for -6z - 2 = -20: z = 3

substitute z = 3

{-25y - 16 * 3 - 8 = 19}

simplify

{-25y - 56 = 19}

isolate y for -25y - 56 = 19: y = -3

for x = -2 - 5y - 5z

substitute z = 3, y = -3

x = -2 - 5(-3) - 5 * 3

-2 - 5(-3) - 5 * 3 = -2

x = -2

x = -2, z = 3, y = -3

2)isolate x for -4x - 5y - z = 18: x = -(18+5y+z)/4

substitute x = -(18+5y+z)/4

{-2(-(18+5y+z)/4) - 5y - 2z = 12}

{-2(-(18+5y+z)/4) + 5y + 2z = 4}

simplify

{(-5y-3z+18)/2 = 12}

{(15y+5z+18)/2 = 4}

isolate y for (-5y-3z+18)/2 = 12: y = -(3z+6)/5

substitute y = -(3z+6)/5

{15((-3z+6)/5)+5z+18/2 = 4}

simplify

{-2z=4}

isolate z for -2z=4: z = -2

for y = - 3z+6/5

substitute z = -2

y = - 3(-2)+6/5

- 3(-2)+6/5 = 0

y = 0

for x = - 18+5y+z/4

substitute z = -2, y = 0

x = - 18+5*0-2/4

- 18+5*0-2/4 = -4

x = -4

x = -4, z = -2, y = 0

3) x = -1, z = -4, y = -4

4) x = 4, z = 0, y = 2

5) r = 1, t = 1, s = 3

6) x = 0, z = -3, y = 0

work for 3, 4, 5, and 6 is below

answer: she must produce at least 9,000 windows in order to make a profit of $48,000

explanation:

48,000 - 12,000 = 36,000

36,000/4 = 9,000

w'x is 0.

hope it