Explanation
We are given the following system of equations:
[tex]\begin{gathered} x-y+z=2\text{ \lparen equation 1\rparen} \\ 2x-3y+4z=4\text{ \lparen equation 2\rparen} \\ -3x+4y+z=0\text{ \lparen equation 3\rparen} \end{gathered}[/tex]
Joe subtracted equation 3 from equation 1 and the result is
[tex]Result:-4x-5y=2[/tex]
We are required to determine if the result is correct or not.
- Since, equation 3 is subtracted from equation 1, this is written mathematically as:
"Equation 1 - Equation 3"
Therefore, we have:
[tex]\begin{gathered} \text{ Equation 1 - Equation 3} \\ \text{ }x-y+z=2 \\ - \\ \text{ }-3x+4y+z=0 \\ \text{ \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_} \\ x-(-3x)-y-(+4y)+z-(+z)=2-0 \\ x+3x-y-4y+z-z=2-0 \\ 4x-5y=2 \\ \\ Note:(-4x-5y=2)\text{ is not }(4x-5y=2) \end{gathered}[/tex]
Hence, the answer is:
[tex]False[/tex]
