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7.1-one - 7.1 Systems of Linear Equations in Two Variables...

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Unformatted text preview: 7.1 Systems of Linear Equations in Two Variables 1. Decide whether an ordered pair is a solution of a linear system. Two linear equations are called a system of linear equations. A solution to a system of linear equations in two variables is an ordered pair that satisﬁes both equations in the system. The solution of a system of linear equations can sometimes be found by graphing both of the equations in the same rectangular coordinate system. For a system with one solution, the coordinates of the point of intersection give the system’s solution. MI nil-H m l- ‘“\<, \“3' "Mill! if . r“ g?“ \.\g‘ 1*2}-'=1. - “QVﬂVC‘ ‘5“ - \‘o‘ *" . {3 7 '\‘2. ‘\\c0 5” “a aﬂ‘: ‘6‘ mm“ .. - \ mew“ \a‘ i‘“ d ' m ‘" com“ 1.1.1693“ td‘m‘t‘“ -, , ‘ ' . l i .1 i “ L x “‘c‘mb “‘ ‘1‘ \ mill“ “in ._t1l‘ _ —” M 1 _ L v ' ‘c All yin: m a . y x \ \$6 “L I wt . mtmﬁ-C' ululim If ___‘ Phi" ﬂ ' “am V‘“ “(Mit- x _ 2y : 5' intermth g I “\‘c‘ 0‘ ' .\ 40"“? t4 1: im \35‘ “ -'\ \“m ' ﬂ‘ ' g I v vcnu i “I!” _ a nlaﬁn. . ?'\“\“ Figure 5.2 L’iaualiring a wilt-slum} minim" If 2. Solve linear systems by substitution. Solving linear Systems by Substitution I. Solve either of the equations for one variable in terms of the other. (If one of the equations is siready it} this fotttt, you can skip this step.) 3. Substitute the expression foqu in step 1 into the other equationﬁhis wit] result in as equation in one variable. 3. Solve the equatitm containing one variable. 4. Back-substitute- the vaiue found in step 3 into one of the original equations. Sim piify and find the mine of the remaining vat-“isms. 5.. Check, the proposed solution in both of the system‘s given. sq nations. Solve the system by the substitution method. .226 + y: 3 (r: I , b" ) Lj:..-—1)<+?> 3x:— ZXLB' ‘ ' “EH—L.) : “7%fo (52X+%)@>::”1? 3:?) TRUE” gx—thé 2—13 "'"3—-—iO'S-ni3 ‘4 X : ,_ :1 «HR : #13 x: :1 Li: «Z(-t)’i3 \ 2.7 4:7) “b 3. Solve linear systems by addition. Suiting Linear Systems by Additima 1. If necessary, rewrite bath equations in the farm Ax + By = C. I. If necessary, multiply either equaiiun or both equatinns by appmpriale nonzem numbers 50 that the sum 0f the x-coefﬁcients or the sum of the y-meffieienls '15- ﬂ. 3.. Add the equatiens in step 2.1116 sum: is an equation in {me vsriahte 4. Salve the equatiun in me variable. 5. Backwsubslilute the value ﬂblained in step 4 ink) either of the give-n equations and suture for the other variable. (i. Check the salutiun in bath of the eﬁginai equalinns. the” Solve the system by the addition method. %+%=1 _(// x y 17 ‘37“? X *l" 2‘ I _ (,3 “5" 3 LCD _ .3 {w L + \$5, : é» a s Bx +33 :— «CD t 5F) 1; 0 vi +'EJ—-:"~L;’; Lcht-LQ) m Lita’fB 1‘ (CS/'7’ 3 a (3 ~ . “a 3 maﬁa): 6 36 3 X": 11 t I «x t M» 4:2, Xt\eyn0/ ('12:) g; +Ltﬁria [L) E’gfn [at] + _._ ,5" -— é” 3 3CX+2)~—2 [5.+q); [8 3x+b 42g ~60; : I8 BX—ly—Q‘ : EXhZHZZO ’—‘@ ‘ gﬁmé} Lab: 10 __ gm - ‘5' ' r b? 7),) mtg-i) W3») 2mm; : SLX"tJ)‘-3\bm 1x+mj —; HEX-«63 #245“ ng +<;[_LJ:, ‘11:; "® B eron& . “PM 5; 9—37“ 3x alt) :20 Solve using either the substitution or the addition method. 8x — 6y = -5 ﬂ —4x+3y=2 ‘62)) @Xl:> LIL ...
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