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# 7.2-one - 7.ZSystems of Linear Equations in Three Variables...

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Unformatted text preview: 7.ZSystems of Linear Equations in Three Variables 1. Verif the solution of a s stern of linear e uations in three variables. PSEE a \$63. Home” 1*” Prebam a I .4, 3, a) .X ﬂ g Hakka) )(‘Slg : ’55 “69 x+3+%:t} ~99 3-3z:~3’@ XFQlj‘E: —@ #Q ,r .. ~33» « h 93119 _ .. ~5" a"lf5; Flﬂ:;_g TRUéh if; L; TRUE ‘ v (:ﬁméD L7 _ /3——3t2>:"3 51—;304)! It are 1’3 afl'ﬁar‘i _3 if?) IRUE 1: (ﬁlm? ch . @ﬁ 2 3 24)-;2 1*” ear/O C ZCZ).‘C—f)‘-3l[?2):*l ’39,“; 1; —L, Lf-y—lw-Qa 11""! :__Ll “TRUE 51,5 :4 r] :1'4WRUtz 4/193 2. Solve systems of linear equations in three variables. An equation such as X+2y—3z=9 is called a linear equation in three variables. In general, any equation of the form Ax + By + CZ = D, where A,B,C, and D are real numbers such that AB, and C are not all 0, is a linear equation in three variables: x,y, and z. The graph of this linear equation in three variables is a plane in three-dimensional space. The process of solving a system of three linear equations in three variables is geometrically equivalent to finding the point of intersection (assuming there is one) of three planes in space. A solution of a system of linear equations in three variables is an ordered triple of real numbers that satisfies all equations of the system. Soiution /, (a) Consistentsystem: so'mions (b) Consistent system; one solution infinite number of solutions (c) inconsistenisystem; no solution Solving Linear Systems in Three Variables by Eliminating Variables I. Reduce the. system to two Equations in two variables'fbis is usually accomplished by taking two different pairs of equations and using the addition method to eliminate the same variable from both pairs- 2. Solve the resulting system of two aquatic-as in: two variables using addition or substitutionfnie result is an equation in one variable that gives the value of. that variabla. 3. Back-substitute the value of the variable found in step '2 into either of the- equations in two variables to find the value of the second variable. 4. Use the values of the two variables from steps 2 and 3 to fin-d the value of the third variable by back-substituting into one of the original Equations 5. Check the proposed solution in each of the original equations. Our initial goal is to reduce the system to two equations in two variables. The central idea is to take two different pairs of equations and eliminate the same variable from both pairs. It does not matter which variable you eliminate, as long as you do it in two different pairs of equations. 1. Solve the system. x+y = 2 "Q 25+ z‘n=-3 M® \. y+z=1r—/C3/ VF ’ g ’2) cw; L " I Mag/“C9 EU" a X+‘j;9\ .___ w—Kj :— “'- _. —— +3 t“[email protected]:)+ )Z-Fb: "3 1 a :; TR!)sz __ 47;: -—‘3 W69 3 6W7 + H: 1 I X+%; — 1 f 21 5’12sz ,3:,; "mug E: “<1 g+22| P[ 4mm %:;-—2 {\ﬂ © “3 a?“ 3,; m H+C”?'7:‘ 1:, (r120: ~11! ...
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7.2-one - 7.ZSystems of Linear Equations in Three Variables...

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