Question

The system of equations 2x +3y -3z = 8, 4x -2y +6z = 9, 10x +3y - 3z = 5 has ----------solution

Answer 1

Answer:

+

38/=8=8=7'"4":47844$4'=4=4/$4$8=8=/8'78

Answer 2

The solution is $(\dfrac{-3}{8}, 7,\dfrac{49}{12})$.

Explanation:

The given system of equations:

$2x +3y -3z = 8----------(1) \\4x -2y +6z = 9-----------(2)\\10x +3y - 3z = 5--------------(3)$

Multiply 2 to equation (1), we get

$4x+6y-6z=16------(4)$

Eliminate (2) from (4), we get

$8y-12z=7------------(5)$

Multiply 5 to equation (1), we get

$10x+15y-15z=40------(5)$

Eliminate (3) from (5), we get

$12y-12z=35------------(6)$

Eliminate (5) from (6), we get

$4y=28\\\\\Rightarrow\ y=7$

Put value of y in (5), we get

$8(7)-12z=7\\\\ 56-12z=7\\\\ 12z=56-7\\\\ 12z=49\\\\ z=\dfrac{49}{12}$

Put value of y and z in (1), we get

$2x+3(7)-3(\dfrac{49}{12})=8\\\\ 2x+21-\dfrac{49}{4}=8\\\\ 2x+\dfrac{35}{4}=8\\\\ 2x=8-\dfrac{35}{4}\\\\ 2x=\dfrac{-3}{4}\\\\ x=\dfrac{-3}{8}$

Hence, the solution is $(\dfrac{-3}{8}, 7,\dfrac{49}{12})$.

# Learn more :

Test for consistency, the given system of equations and solve, if it is consistent.

7x+2y+3z=16

2x+11y+5z=25

x+3y+4z=13

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