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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Step-by-step Solution
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. \( x=0 ; y=0 ; z=3 \).
Quick Answer
La solución es \( x=0 ; y=0 ; z=3 \). La respuesta correcta es a.
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