Solve the system by elimination 1: x+5y-4z=-10, 2x-y+5z=-9, 2x-10y-5z=0 .. . 2. Solve the system by substitution: 2x-y+z=-4, z=5
, -2x+3y-z=-10. . . 3. A food store makes a 11–pound mixture of peanuts, almonds, and raisins. The cost of peanuts is $1.50 per pound, almonds cost $3.00 per pound, and raisins cost $1.50 per pound. The mixture calls for twice as many peanuts as almonds. The total cost of the mixture is $21.00. How much of each ingredient did the store use?
1 ) 1st and 2nd equation (multiply 1st by -2 ): -2x - 10 y + 8 z = 20 2 x - y + 5 z = -9 --------------------------- - 11 y + 13 z = 11 / * ( -20 ) 1st and 3rd: - 2 x - 10 y + 8 z = 20 2 x - 10 y - 5 z = 0 ----------------------------- - 20 x + 3 z = 20 / * 11 ---------------------------------- 220 y - 260 z = -220 - 220 y + 33 z = 220 ------------------------------ z = 0, y = -1, x = - 5 2 ) 2 x - y + 5 = -4 - 2 x + 3 y - 5 = - 10 Substitution: y = 2 x + 9 - 2 x + 3(2 x + 9 ) = -5 4 x = - 32, x = -8, y = -7, z = 5 3 ) x + y + z = 11 1.5 x+3 y +1.5 z = 21 x = 2 y ------------------------ 3 y + z = 11 / * (-2) 6 y + 1.5 z = 21 ------------------------ - 6 y - 2 z = -22 6 y + 1.5 z = 21 ------------------------ -0.5 z = -1, z = 2, y = 3, z = 6 Answer: the store used 6 pounds of peanuts, 3 pounds of almonds and 2 pounds of raisins.
