Potter Osborne
08/28/2024 · Senior High School

La solución del siguiente sistema es: \( \left.\begin{array}{c}2 x+y-z=-3 \\ 3 x-y+z=3 \\ 5 x+4 z=12\end{array}\right\} \) a. \( x=0 ; y=0 ; z=3 \) b. \( x=5 ; y=25 ; z=30 \) c. \( x=5 ; y=20 ; z=5 \) d. \( x=3 ; y=0 ; z=0 \)

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Solve the system of equations \( 2x+y-z=-3;3x-y+z=3;5x+4z=12 \). Solve the system of equations by following steps: - step0: Solve using the substitution method: \(\left\{ \begin{array}{l}2x+y-z=-3\\3x-y+z=3\\5x+4z=12\end{array}\right.\) - step1: Solve the equation: \(\left\{ \begin{array}{l}y=-3-2x+z\\3x-y+z=3\\5x+4z=12\end{array}\right.\) - step2: Substitute the value of \(y:\) \(\left\{ \begin{array}{l}3x-\left(-3-2x+z\right)+z=3\\5x+4z=12\end{array}\right.\) - step3: Simplify: \(\left\{ \begin{array}{l}5x+3=3\\5x+4z=12\end{array}\right.\) - step4: Solve the equation: \(\left\{ \begin{array}{l}x=0\\5x+4z=12\end{array}\right.\) - step5: Substitute the value of \(x:\) \(5\times 0+4z=12\) - step6: Simplify: \(4z=12\) - step7: Divide both sides: \(\frac{4z}{4}=\frac{12}{4}\) - step8: Divide the numbers: \(z=3\) - step9: Substitute the values of \(x,z:\) \(y=-3-2\times 0+3\) - step10: Simplify: \(y=0\) - step11: Calculate: \(\left\{ \begin{array}{l}x=0\\y=0\\z=3\end{array}\right.\) - step12: Check the solution: \(\left\{ \begin{array}{l}x=0\\y=0\\z=3\end{array}\right.\) - step13: Rewrite: \(\left(x,y,z\right) = \left(0,0,3\right)\) La solución del sistema de ecuaciones es \( x=0, y=0, z=3 \), por lo tanto, la respuesta correcta es a. \( x=0 ; y=0 ; z=3 \).

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La solución es \( x=0 ; y=0 ; z=3 \). La respuesta correcta es a.
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