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DATE NAME 7-4 PERIOD Study Guide and Intervention - Elimination Using Multiplication Elimination Using Multiplication Some systems of equations cannot be solved In such cases, one or both equations must the equations. by adding or subtracting simply first be multiplied by a number before the system can be solved by elimination. ru ffi r*105r=3 4fi + 5Y:5 2r use elimination to solve the system of equations. use elimination to solve the system of equations. If you multiply the second equation by you can eliminate the y terms. (+) 3x-2y--7 - 5Y: lg If you multiply the first equation by 2 and the second equation by -3, you can eliminate the r terms. -2, x*I}Y: 3 : 10y -10 -8r : -7 -7x -7x -7 -7 -7 -:-)c:l 6x- 4Y:-14 : -30 71Y : -44 11v -44 11 11 !:-4 (+) -6.r + 15y I for x in either equation. 1+10y:3 1+10y-1-3-1 IOY=2 l}y=2 10 10 1 \) :: Substitute The solutio" Substitute -4 for y in either equation. 3x-2(-4):-7 3r*8--7 3r+8-8:-7-8 3r : -15 3x -15 33 -:x: -5 i. (r, f). The solution is (-5, -4). reFlffirlc Use elimination to solve each system of equations. L,2x+3y:6._il ,r\ x1-2Y=$ '-''"i! 4.4x+5Y:6 , t r\ 6x - 7y : -20 '.-i' {'r 7"4s-t9 .r -i\ " 5s * 2t:8 t'j -: i 10.6r-4y: -8,-i,d'i i':l 4x+2Y:-3' *.3: : 4- i _i. I ) -trL*2n:5 \ 2r.2rn 5.1, - 39 :-?2 ' ;+. .]) t: 2c-d=I0 8.4a-3b:-8r-.L i 2a + 2b:3 rl ,! l1-.4x*2y:-5r i- .j-\ -%c - 4Y : L '-t]' 'l ' - b :2 "i''iti\ a+2b:3 6.3x-4y:-4.*,; -jir'/ x*3Y = -10 9.2x + 2y:5 I il ir) 4x-4Y:L0'J't -'' 3.3a Lzt2x +y:3.5 '" -x -l 2Y : 2.5 13: GARDENING The tength of Sally's garden is 4 meters greater than 3 times the width. ''" The perimeter of her garden is 7i meters. What are thetimensions of Sally's garden? '1 14. .i'* tTi (,'4 Anita is f ,1 {f; years older than Basilio. Three times Anita's age added to six times Basilio's ase is 86. How old are s Glencoe/McGraw-Hill Anita and Basilio? Hnl 421 tt .i . T f":iurirc i; Glencoe Algebra 1 PERIOD Study Guide and Intervention pontinued) Elimi nation Using M ultiplication Determine the Best Method The methods to use for solving systems of linear equations are summarized in the table below. The Best Time to Use Method Graphing to estimate the solution, since graphing usually does not give an exact solution Substitution if one of the variables in either equation has a coefficient of 1 or Elimination Using Addition if one of the variables has opposite coefficients in the two equations Elimination Using Subtraction if one of the variables has the same coefficient in the two equations Elimination Using Multiplication if none of the coefficients are 1 or -1 and neither of the variables can be eliminated by simply adding or subtracting the equations -1 reDeterminethebestmethodtosolvethesystemofequations.Then solve the system. &r+2Y=20 -?.s+4Y=-16 Since the coefficients of r will be additive inverses of each other if you equation by 3, use elimination. 6x + 2(-2) : 20 20 6x multiply the * 2Y: (+) -Gx + L2y : -48 : -23 L4y -28 L4 - 14 L4Y y:-2 substitute second -2lor yin either equation. Multiply the second equation by 3. Add the tvvo equations. x is eliminated. 6x Divide each side by 14. 6x - 4:20 - 4 + 4 = 20 + 4 6x:24 6x _24 Simplify. 66 x:4 simptify. Add4toeachside, Simplify. Divide each side by 6. Simplify. The solution is (4, -2). Determine the best rrqgthgl to solve each system of equations. Then solve the system. l.x-2y:3 t i r\ \--lt7J X-!:1 2.m*6n:-8 m:2nt8 4.4x+y:I5 t1.j) -x-3Y:-I2"- 5.3c 7.4x: 8.x: -2y 2y - 70: X-l 2Y=$ i) \ -iii'''l - 4b: 2a*4b: -]o i-.. 5) LO.4a o Glencoe/McGraw-Hill r,, a\ '..-f,-'t,) 1-'t: t"i'' : -G t-1 -2x-10Y=2\'i' LL.4x + 10Y 422 {i.l \"-' -i\tl * 2y: -e [-i, -'i] y=M .. - d: L4 iL,'l) "'i"--f,: r'* 4x + 4y -- -10 3.a-b:6 a=2b*7 6.x r .J "i\ ^t,/ tl 9.2s-3t:42 i \ .r'\ Bs * 2t : 24 i.Ii'*tt,l u' ?*:*'r-:to t' i, -*'i ) Glencoe Algebra 1 PERIOD DATE Skills Practice Elimination Using Multiplication Use elimination to solve each system of equations. * 2Y: -g x-Y = -13 L.x * !: -9 - 2Y :12 i.j, -ll/ 3.?.rc + 5y:3 -x*3y--7 2.3x 5x lt' i4,\ | * ft J I, , L,J \ ;.t Brl 4.?e, + {1,,i O -n " ,V,nr 7.5x+3y:-10 8.2x + 3x+5y--6 3Y: 14 3x-4Y:4 !;''1 -l\ :lf i*] \ .r. lt\ v.r 9.2* - 3Y:2L i t ir\ r i -., - l\ 6.2'x + Y ;-t ;i 5x .. : 5x*3Y:) 6.4tc-2Y:-L4 3r-Y:-g 2Y 3 -4x-4Y:-8 ,\ I \ y= L 10.3r*2Y:-26 4x-Ey--4 :25 i r t. "5) . \-' ,,\ }|A: il : -3 3x*3y:9 11.3r-6y:-3 ?.tc + 4Y :30 12,5x ;? i) ..1 +/ 'f 2Y i-.11.) --_'-,w) ,13. TWo times a number plus three times another number equals 13. The sum of the two * numbers is 7. What are the numbers? "-+ ..14. *' .inil - | Four times a number minus twice another number is is -1. Find the numbers. - 16. The sum of the two numbers -:t ittr,.i ,i o,i-lr.Si Deterrnine the best mg!Ig_4 to solve each system of equations. Then solve the system. ;..15J% * 3y:19 5x+2y--8 wv:2* 3x + 2Y :35 itg; gr - 4y "'' 4x + 5y : L7 :2 o Glencoe/McGraw-Hill /*L& 41 r f*rl 116,8r-7y=78 {i+ ''3r+7Y:26 ''til t) / l- l/'r) ty:6 !8i3r " 3x*!:3 -;) t?Oiy: 3r * ('t1, '3x-y:-l 423 {lrJ L .',11il ililfl rnfrfi itQirJ rtYJng -;"rL]ti 0{l5 Glencoe Algebra 1 DATE NAME PERIOD - Practice Elimi nation Using Multiplication Use elimination to solve each system of equations. Y: -I 3x-2Y:1 2.5x t.2x - - 2Y: 3.7x -t 4Y : -4 lrc + 8y :28 -10 3x-f 6Y:$6 ; i,-1" -5) 4.2x-4Y:-22 3rtBY:$g 5x-3Y:L6 n\ 1 l,*j) - lp: -, x+fl:0 * O.5y : -2 id:o rr \ -3x-5Y:-IL ul, -il {.2';2"*4y:27 * v t.-r"i, 5.3r*2Y:-g 5x-BY:4 {,-'},7) :, tl 6.4x-2Y:32 i-:], lL)) qojzr 1 \+ ",6) i,br3) j,4l ,_ 4 i " '.\ times a number plus frve times another number is -13. The sum of the two ifOlnignt \-" numbers is 1. What are the number^t * * sI i, ullli T another number equals 4. Three times the first number plus four times the other number is 7. Find,the numbers. t*o times a number plus three times iff: uJ 1j' ..r'; *1 Determine the u"#r#Strrod to solve system. 'f 7Y : 3 2x-7Y: -38 L2.5x i!E]* : 2y + """n "i"tff'1, .n1r",rons. Then solve the t-y,,1) i};T;:A=r_r, y;,,6) tn. -u.*;fl:_t, i-1, -{) 6 lntrni'i-Vlil [9i- & -t 3y :: -2 t:u'i}lLlfll,Rl{ir'-: lr* 4x + 3Y 3 (.t-,,3J '*. i' -, : t ifrl tJ f lfrfnfrf CE Gunther invested $10,000 in two mutual funds. One of the funds rose 67o in orru year, and the other rose 97o in one year. If Gunther's investment rose a total of $684 in one year, how much did he invest in each mutual fund? 1 ='x - 2Y :9 5 ffll{ly n't'r"r'n; $? iuu rn thu ul, tlinli ul'{.l S )silli ,il tnt 4 t: 'hr"rn'"i ifb. C4TOEING Laura and Brent paddled a canoe 6 miles upstream in four hours. The "'-' return trip took three hours. Find the rate at which Laura and Brent paddled the canoe in stiil water. 1.75 {npn €0, trtUMgER THEORY The sum of the digits of a two-digit number is 11.If the digits are '- 1."u"rr"d, the new number is 45 more than the original number. Find the number. o Glencoe/McGraw-Hill Glencoe Algebra 1