Question

Classify the system and identify the number of solutions.4x + 3y - 4z = 43x + 5y + 2z = 97x + 4y - 6z = 1

Answer 1

Given,

The pair of the equations is,

`\begin{gathered} 4x+3y-4z=4 \\ 3x+5y+2z=9 \\ 7x+4y-6z=1 \end{gathered}`

The situation of no solution is,

`((a_1)/(a_2))/(a_3)=((b_1)/(b_2))/(b_3)\\e\frac{\frac{c_1}{c2_{}}}{c_3}`

The situation of unique solution is,

`((a_1)/(a_2))/(a_3)\\e((b_1)/(b_2))/(b_3)\\e\frac{\frac{c_1}{c2_{}}}{c_3}`

The situation of infinite solution is,

`((a_1)/(a_2))/(a_3)=((b_1)/(b_2))/(b_3)=\frac{\frac{c_1}{c2_{}}}{c_3}`

So, the equation have unique solution or one solution.

Hence, option A is correct.