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Use any convenient method to solve the following system of equations. If the system is dependent, express the solution set in terms of one of the variables. Leave all fractional answers in fraction form.
2x−2y+6z=163x+3y−4z=−5x−y+3z=9

Respuesta :

For a solution to be the solution to a system, it must satisfy all the equations of that system. There exists no solution for the system of equations.

What is a solution to a system of equations?

For a solution to be the solution to a system, it must satisfy all the equations of that system, and as all points satisfying an equation are in their graphs, so solution to a system is the intersection of all its equation at a single point(as we need a common point, which is going to be the intersection of course)(this can be one or many, or sometimes none)

For the three equations,

2x−2y+6z=16

3x+3y−4z=−5

x−y+3z=9

Solve the first equation for x,

2x−2y+6z=16

x = 8 + y - 3z

Now substitute the value of x in both the equations, if the two equations are satisfied, then the equation will have a solution, if it's not then no solution exists.

[tex]3\left(8+y-3z\right)+3y-4z=-5\\6y-13z+24=-5\\\\\\ 8+y-3z-y+3z=9\\ 8=9[/tex]

Hence, There exists no solution for the system of equations.

Learn more about the System of equations:

https://brainly.com/question/12895249

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