Solving Systems of 3 Equations

Solve each system of three equations: (a) (b) (c) x + y + z = 2 2x + y + z = 9 x + 3y + 4z = 14 2x + y – z = 5 -x – y + z = 1 2x – 3y + 2z = 10 x – y + z = -2 3x – y + z = 9 3x – y + z = 9

(d) (e) (f) 4x – y + 3z = -2 x + 2y + 3z = 8 3x – 2y – 8z = 1 3x + 5y – z = 15 3x – y + 2z = 5 9x – 6y – 24z = -2 -2x + y + 4z = 14 -2x – 4y -6z = 5 x – y + z = 1

(g) (h) (i) 2x – 4y + z = -4 4x – 3y + z = 9 x + 4y – z = 6 x + 2y – z = 0 3x + 2y – 2z = 4 2x – y + z = 3 -x + y + z = 6 x – y + 3z = 5 3x + 2y + 3z = 16

(j) (k) (l) 3x + y – z = 7 a – 3b – 2c = -3 2x + 2y + 2z = 6 2x – 3y + z = -7 3a + 2b – c = 12 3x – 3y – 4z = -1 x – 4y + 3z = -6 -a – b + 4c = 3 x + y + 3z = 11

ANSWERS: (a) (1,2,-1) (b) (2,1,4) (c) (2,0,3) (d) (-1,4,2) (e) no solution (f) no solution (g) (0,2,4) (h) (2,0,1) (i) (1,2,3) (j) (2,5,4) (k) (4,1,2) (l) (2,-3,4)

Solving Systems of 3 Equations

Solve each system of three equations: (a) (b) (c) x + y + z = 2 2x + y + z = 9 x + 3y + 4z = 14 2x + y – z = 5 -x – y + z = 1 2x – 3y + 2z = 10 x – y + z = -2 3x – y + z = 9 3x – y + z = 9

(d) (e) (f) 4x – y + 3z = -2 x + 2y + 3z = 8 3x – 2y – 8z = 1 3x + 5y – z = 15 3x – y + 2z = 5 9x – 6y – 24z = -2 -2x + y + 4z = 14 -2x – 4y -6z = 5 x – y + z = 1

(g) (h) (i) 2x – 4y + z = -4 4x – 3y + z = 9 x + 4y – z = 6 x + 2y – z = 0 3x + 2y – 2z = 4 2x – y + z = 3 -x + y + z = 6 x – y + 3z = 5 3x + 2y + 3z = 16

(j) (k) (l) 3x + y – z = 7 a – 3b – 2c = -3 2x + 2y + 2z = 6 2x – 3y + z = -7 3a + 2b – c = 12 3x – 3y – 4z = -1 x – 4y + 3z = -6 -a – b + 4c = 3 x + y + 3z = 11

ANSWERS: (a) (1,2,-1) (b) (2,1,4) (c) (2,0,3) (d) (-1,4,2) (e) no solution (f) no solution (g) (0,2,4) (h) (2,0,1) (i) (1,2,3) (j) (2,5,4) (k) (4,1,2) (l) (2,-3,4)