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Sagot :
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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