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Select the correct answer. What is the solution to this system of equations? 3⁢x+6⁢y−5⁢z=29-9⁢x+y+4⁢z=9-8⁢x+7⁢y+5⁢z=4

Sagot :

rafikiedu14

y=-20, x=-1, c= -5

SOlution :

three-by-three systems:

In order to solve systems of equations in three variables, known as three-by-three systems, the primary goal is to eliminate one variable at a time to achieve back-substitution. A solution to a system of three equations in three variables x,y,z

is called an ordered triple.

To find a solution, we can perform the following operations:

Interchange the order of any two equations.

Multiply both sides of an equation by a nonzero constant.

Add a nonzero multiple of one equation to another equation.

HOW TO: GIVEN A LINEAR SYSTEM OF THREE EQUATIONS, SOLVE FOR THREE UNKNOWNS.

Pick any pair of equations and solve for one variable.

Pick another pair of equations and solve for the same variable.

You have created a system of two equations in two unknowns. Solve the resulting two-by-two system.

Back-substitute known variables into any one of the original equations and solve for the missing variable.

3⁢x+6⁢y−5⁢z=29...(1)

-9⁢x+y+4⁢z=9...(2)

-8⁢x+7⁢y+5⁢z=4...(3)

Solving 1&2

3x+6(9-4z+9x)-5z=29

3x+54-24z+54x-5z=29

57x+54-29-29z=0

57x+25-29z=0

57x-29z=25...(3)

Solving  2& 3

-8x+7(9-4z+9x) +5z=4

-8z+63-28z+63x+5z=4

55x-23z-59=0 ..(4)

Solving 3 & 4

57x-29z=25...(3)

55x-23z-59=0 ..(4)

(55x29-57x23)x=59x23-25x23

-2906x = 2906

x=-1

putting it on equation 4

55x-23z-59=0 ..(4)

55(-1)-23z-59=0 ..(4)

z= - 5

-9⁢(-1)+y+4⁢(5)=9.

9+y+20=9

y=9-20-9

y=-20

More Details :brainly.com/question/24147772

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