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# 7.4 - 7.4 S stems of Nonlinear E nations in Two Variables 1...

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Unformatted text preview: 7.4 S stems of Nonlinear E nations in Two Variables 1. Recognize systems of nonlinear equations in two variables. A system of two nonlinear equations in two variables, also called a nonlinear system, contains at least one equation that cannot be expressed in the form Ax+By=C. Isl-inﬁll“ gt , , ' Hailh'lrsplin' iii! _' ‘ﬂ‘ = 23’ + 10 ‘M-i-HTFC; 3" = x” + 3 ﬁﬁmﬂx'4+ﬂy"—f€t A solution of a nonlinear system in two variables is an _ a} ' - . . . CMEC {C} j 3 ‘1 ordered pan of real numbers that satisﬁes both equatlons / I in the system. The solution set of the system is the set of x’; 9J1 —;_ l t) 19:— 2b) all such ordered pairs. Xi éx—rl‘? :10 Y‘lﬁéx + ‘3" ”7* D CX—LWPSU :0 x_|+:é X‘ZT—O 2. Solve nonlinear systems by substitution. The substitution method involves converting a nonlinear system to one equation in one variable by an appropriate substitution. The steps in the solution process are exactly the same as those used to solve a linear system by substitution. Since at least one equation is nonlinear you may get more than one point of intersection. Solve the system by the substitution me od. FIE, '- 1 +5 0 (Have: I xy ; 8 ——® 0 '— X+_§:C.+(;:O %:C3TRUL 9' C23 XL-r‘s—t-ﬁXT— #f—Lfekéro Xpri-éXi—‘g 2‘— Qiorygug KX-Ht)(lx+1):0 Xi— ~01 \ Piaf I; X214} in. €fm® Pluf w X251 in gSnQ) -—lf.3:8 “‘25”; g 3. Solve nonlinear systems by addition. For nonlinear systems, the addition method can be used when each equation is in the form AX2 + By2 2 C. If necessary, we will multiply either equation or both equations by appropriate numbers so that the coefﬁcients of xzor y2 will have a sum of 0. Again you may get more than one point of intersection. Solve the system by the addition method (0 R) L [inane—it mCiJﬁt , , 35‘ x —3y= 10 -————® X : txiﬁllf x22+y =50 —-'[email protected] XZ+1JW XLtieji/nCDbUWI § 'h‘ .. 2‘ 5";[0 MVQD 1+3; :50 X:3() l xﬂlbﬁﬁlo '2. 0 "2.. p. 34—33 L!- X 19—") L Lj—l—Bj—atf020 XZib‘.’ Che. [C C LLCU. u (him: AK) K6: 5) £2.33 —:. [‘0 wxlgyi : i 0 ml— 3 w = ,0 6mm 0 2— L") (Mr) 1- 74E 2 to lo 2 to «2. L (W) +24: 0 @311: 5‘0 ”14+?”er 7’ ‘1‘; , (0::0‘1‘Rué“ 5+5 :50 (43%;): X535 ‘9 0 L—m—gﬁ:ao w ~ 0 9— ._ L—L) ULHJFM :bo ELM) 4—H} “-1 60 go :60 TRUE" 2"__3t1 :: [’0 CH5?“- 3 L6“) = [0 57...”; 2 (“O 3. Solve problems using systems of nonlinear equations. ax”: 69x +420 :0 at left. Ifyou have to enclose msquare yards, whata X; +5110) 0 ———: _.. 2 WGEL' are the dimensions of the enclosure? (2 19X CEL/d Q (I6)+3\(29 ) 2 5‘3 X —7_«=)x +210 2 o as 7:. 5‘8 TR”; ‘ OCH”) (HQ) '2 0 X: [5* 1 €°Y‘@ [15“- 1% :1Cpo ’ Li *5” - MW ~ h (ram-.7 xcf‘mg :rqo - . 55597.5 ”75a, XZW 1qu 12 um " to The sum between the squares of two numbers is 25. The square of the first number minus two times the square of the second number i - Find the numbers. ...
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7.4 - 7.4 S stems of Nonlinear E nations in Two Variables 1...

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