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Unformatted text preview: 4.2 Solving Systems of EquaTions in Three Variables Goal: Solve Thr'ee equaTions wiTh Thr'ee unknowns The soluTion of a linear equation in Three variables is an ordered
Triple (x, y, 2) That makes The equaTion True. HW problem #1: Which equaTions have (4, 3, 1) as a soluTion? '7 = I5Hi3
a)x+Y+z 3 + 3.23 7
b)x+y+z=5 ‘("13+3+‘;:5 I43‘H "*5
5=S?
c)—x+y+22=0 ‘(”‘)+3+Z(‘):O
l+$+ZéO biovqn.
\+7_(?>)3(l31;2 , .3%Z
“L” 2:2 We can use eliminaTion or' subsTiTuTion To solve a sysTern of Three
equa’rions, jusT like we did wiTh a SysTem of Two equaTions. d)x+2y3z=2 Solving a System of Three Equations using Elimination:
Step 1: Write each equation in standard form Ax + By+ 62 = D Step 2: Choose a pair of equations and add them to eliminate a
variable. Step 3: Choose another pair of equations and add to eliminate the
same variable as in step 2. Step 4: Solve the resulting system of two equations for both
variables. Step 5'. Substitute the values of the two known variables into any
of the original equations and solve for the third variable. AAA®+©‘
HWproblem#5: G) x—y+z:4 @XﬂY‘lEf'q
©3x+2y~zz5 ©3¥+2v—Z—5
©~2x+3yz=15 @qx W ..—_ \ é—rnuHiplwbﬁ
®*8¥'2\{: Homework: p. 233 #116 Now (Julio @ J‘@ ...
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This note was uploaded on 05/13/2011 for the course MTH 110 taught by Professor Helenius during the Spring '08 term at Grand Valley State University.
 Spring '08
 HELENIUS

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