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

Classify The System And Identify The Number Of Solutions4x 3y 4z 43x 5y 2z 97x 4y 6z 1 class=

Sagot :

Given,

The pair of the equations is,

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

The situation of no solution is,

[tex]\frac{\frac{a_1}{a_2}}{a_3}=\frac{\frac{b_1}{b_2}}{b_3}\ne\frac{\frac{c_1}{c2_{}}}{c_3}[/tex]

The situation of unique solution is,

[tex]\frac{\frac{a_1}{a_2}}{a_3}\ne\frac{\frac{b_1}{b_2}}{b_3}\ne\frac{\frac{c_1}{c2_{}}}{c_3}[/tex]

The situation of infinite solution is,

[tex]\frac{\frac{a_1}{a_2}}{a_3}=\frac{\frac{b_1}{b_2}}{b_3}=\frac{\frac{c_1}{c2_{}}}{c_3}[/tex]

So, the equation have unique solution or one solution.

Hence, option A is correct.

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