Answered

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Solve the system of equations. If the system has no solution, say that it is inconsistent.

Solve The System Of Equations If The System Has No Solution Say That It Is Inconsistent class=

Sagot :

Answer:

D. The system is inconsistent

Step-by-step Explanation:

Given the below system of equations;

[tex]\begin{gathered} 2x-2y+5z=11\ldots\ldots\ldots\text{Equation 1} \\ 6x-5y+13z=30\ldots\ldots\ldots\text{.}\mathrm{}\text{Equation 2} \\ -2x+3y-7z=-13\ldots\ldots\ldots\text{Equation 3} \end{gathered}[/tex]

We'll follow the below steps to solve the above system of equations;

Step 1: Add Equation 1 and Equation 3;

[tex]\begin{gathered} (2x-2x)+(-2y+3y)+(5z-7z)=(11-13) \\ y-2z=-2 \\ y=2z-2\ldots\ldots\text{.}\mathrm{}\text{Equation 4} \end{gathered}[/tex]

Step 2: Multiply Equation 3 by 3, we'll have;

[tex]-6x+9y-21z=-39\ldots\ldots\text{.Equation 5}[/tex]

Step 3: Add Equation 2 and Equation 5, we'll have;

[tex]4y-8z=-9\ldots\ldots\ldots\text{Equation 6}[/tex]

Step 4: Put Equation 4 into Equation 6 and solve for z;

[tex]\begin{gathered} 4(2z-2)-8z=-9 \\ 8z-8-8z=-9 \\ 8z-8z=-9+8 \\ 0=-1 \end{gathered}[/tex]

From the above, we can see that we do not have a solution for z, therefore, we can say that the system of equations has no solution, hence, it is inconsistent.

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