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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. Islinﬁll“ gt , , ' Hailh'lrsplin' iii! _' ‘ﬂ‘ = 23’ + 10 ‘MiHTFC; 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
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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
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" 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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 Fall '11
 BlisinHestiyas

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