Answer to Question #175581 in Linear Algebra for william

Question

solve the system of three variable linear equations.

4x - 2y + 3z = 1

x + 3y - 4z = -7

3x + y + 2z = 5

Answer 1

4x - 2y + 3z = 1

x + 3y - 4z = -7

3x + y + 2z = 5

x= -3y+4z-7

4(-3y+4z-7)-2y+3z=1

3(-3y+4z-7)+ y+2z=5

-14y+19z=29

-8y+14z=26

z=(29+14y)/19=(26+8y)/14

$29\cdot 14+14\cdot 14y=26\cdot 19+8\cdot 19y$

44y=88

y=2

z=(26+8y)/14=3

x=-3y+4z-7=-1

Answer. x=-1, y=2, z=3.