11.2E: Sistemas de Ecuaciones Lineales con Tres Variables (Ejercicios)
- Page ID
- 111912
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Para los siguientes ejercicios, resolver el sistema de tres ecuaciones mediante sustitución o suma.
11.
\(0.5 x-0.5 y=10\)
\(-0.2 y+0.2 x=4\)
\(0.1 x+0.1 z=2\)
12.
\(5 x+3 y-z=5\)
\(3 x-2 y+4 z=13\)
\(4 x+3 y+5 z=22\)
13.
\(x+y+z=1\)
\(2 x+2 y+2 z=1\)
\(3 x+3 y=2\)
14.
\(2 x-3 y+z=-1\)
\(x+y+z=-4\)
\(4 x+2 y-3 z=33\)
15.
\(3 x+2 y-z=-10\)
\(x-y+2 z=7\)
\(-x+3 y+z=-2\)
16.
\(3 x+4 z=-11\)
\( x-2 y=5\)
\(4 y-z=-10\)
17.
\(2 x-3 y+z=0\)
\(2 x+4 y-3 z=0 \)
\(6 x-2 y-z=0 \)
18.
\(6 x-4 y-2 z=2 \)
\(3 x+2 y-5 z=4 \)
\(6 y-7 z=5\)
Para los siguientes ejercicios, escriba un sistema de ecuaciones para resolver cada problema. Resolver el sistema de ecuaciones.
19. Tres números impares suman hasta 61. Cuanto menor es un tercio más grande y el número medio es 16 menos que el mayor. ¿Cuáles son los tres números?
20. Un teatro local se agota para su espectáculo. Venden todos los 500 boletos por un monedero total de\(\$ 8,070.00 .\) Los boletos tenían un precio\(\$ 15\) para estudiantes,\(\$ 12\) para niños, y\(\$ 18\) para adultos. Si la banda vendió tres veces más boletos para adultos que boletos infantiles, ¿cuántos de cada tipo se vendieron?