Question

Solve using Cramers Rule xty - 2 =o 2 4x -y +22 =30 (2) 1x +-42 = -15 )

Answer 1

solution: Given system of equations x +y - 2 = 0 4X - Y +22=30 x + y - 42 = -15 Here the coefficient matrix is 1 1 1 -1 A = 1 4 1 2 | 1 1 - 4 and deta= 1 4 1 – l - 1 2 l - 4 = 1(4-2) -4 (-4+1) +1(2-1) - 1(2) – 4(-3) 1 (1) - 2 + 12 +1 = 15 to Therefore there exists a unique solution for X, Y, Z. 10 € -1 30 – 1 2 By Cramer's sule, x = 1-15 l - 4 det A 8(4-2)-30 (-4+1)-15. (2-1) 15

=> x = 0-30(-3) -15(1) 15 90 - 15 15 75 c 15 - 5 1 o 4 30 1 - 15 det 1 2 -4 A 1(-120+30)-4 (0-15)+1(8+30) 15 - 90 +60 +30 15 = 0 4 11 1 1 30 1 15 det A Z - 11 1 (15-30) ~41-15-0)+1(30-0) 15 - 15 +60 +30 15 - 15 +90 - 7 = 5

Therefore the X= 5 , y = 0 solution is , Z = 5.