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  • Solve the system of equations                         x + y + z = 6 <

Solve the system of equations

                        x + y + z = 6

                        x + 2y + 3z = 14

                        x + 4y + 7z = 30 has

Your Answer:

unique solution

Option 1:

no solution

Option 2:

unique solution

Option 3:

infinite solutions

Option 4:

none of these

Correct Answer:

infinite solutions

Answers (1)

given that

three equations

\\ x + y + z = 6\\ x + 2y + 3z = 14\\ x + 4y + 7z = 30\\

find: correct option

solutions:

separate the variables

x=6-y-z\\ \text{put it in other two equations}\\ 6-y-z+2y+3z=14 \Rightarrow\ y+2z=8\\ 6-y-z+4y+7z=30 \Rightarrow\ y+2z=8\\ \text{we can observe that both equations are same}\\ \text{that mean system of equation have infinite solutions}

Hence, option 3 (infinite solution) is correct.

Posted by

Ramraj Saini

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