Using Algebraic Methods to Solve Linear System

Name_�------------- Date_______ Class _______ Practice В Using Afgebraic Methods to Solve Linear Systems Use substitution to so!ve each system of equations. 1. 2х -Зу=14 {Х=7у-4 2 • Зх 5 {у2х-=Зу+ = 6 Зх - 4у = 20 3. { у -2х = О Use elimination to solve each system of equations. х+6у=1 4. { Зх+Sу=-10 Зх+4у=6 5. { 2х +Зу= 3 Зх -Sy = 1 6. { 2х+Зу=-12 Use substitution ог elimiпation to solve each system of equations. 7. { х +у= 13 2х -Зу=1 х = -Ву 1 О. { х +у= 14 8. 9х+2у = 5 { Зх- =-10 у 2х + 4у = 12 11 _ { -Зх+Зу=63 9. { 2х +у= 1 Х=5+у 5х-2у=-1 12. { Зх - у= -2 Solve. 1 �l•ti--!�es his house fог Makayla's house riding his Ьicycle at 8 miles р�г houi:--дlthe �ame time_, Makayla leaves hег house heading toward B1ll's house waik�3 m1les рег hour. а. Write а system от �11ations to represent the distance, d, each is from Makayla's house in hhow: . They live 8.25 miles apart. Ь. Solve the system to determine how long they • . vel before meeting. Class _______ Name ________________ Oate ____ ___ Practice С Usfng Algebraic Methods to Solve Linear Systems Use substitution or elimination to solve each system of equations. 1. Jx=y-5.2 l 2х +Зу= 9.6 2х + 20у = 3 4. { 2х =-7у -1 О 7. {з2х +Зу= 42 4 5х =4у l fx+4y=2 4 4х-3у=39 1 Х=у+2 з. х +у= 5 Зх + 2у= 4 Зх+4у=35 6. { 4х-2у=21 5х-5у=6 { 4х + 7у =-4 2х-8у=24 9. { х-21=16у 2. { 5. { 8. Зх-4у=5 So!ve. 1О. Сога bought 4 pounds of nuts and 2 pounds of raisins for $23.50. Mark bought 2 pounds of nuts and 4 pounds of raisins for $18.50. а. Write а systen1 of equations that represents the price of the nuts, п, and the price of the гaisins, г. Ь. Solve the system. How much should а pound of nuts and а pound of raisins cost together? 11. Kate and Riley аге reading the same book. Kate reads 23 page рег 111inute, and Riley гeads � page рег minute. Kate has already 4 read 70 pages, while Riley has read 30 pages. lf they both resume reading together, eveпtually Riley will catch up to Kate. а. Оп what page will that occur? Ь. How many minutes !1ave they read when Riley catches up? Name _______________ Date _______ Class _______ ProЫem Solving Using Afgebraic Methods to Sofve Linear Syste1ns Shanae mixes feed for various animals at the zoo so that the feed has the right amount of protein. Feed Х is 18% protein. Feed У is 10% protein. Use this data for Exercises 1-4. � ow much of each feed should Shanae mix to get 50 lb of feed а.� ite а linear system of equations. Ь. Solve---the system. How much of each feed should ? � at is 15% protein? ----;"------------- 2. Shanae has 15 lb of Ped У left. She wants t make а mixture that is 12% protein. She needs to know how muc:s of Feed Х to use and how much of the mixture she сап make. а. Write а linear system of uations Ь. How much of Feed Х should с. How much of the mixtur ill she ake? Choose the !etter for the Ье 3. Feed У. Which equ ion gi\1es the percent of protei (с) in the mixture? А 12(0.1� + 20(0.10) = 32с В 32[1 ?('О.18) + 20(0.1О)]= с с 12(о_18) + 20(0.10) = с 9112(0.18) + 20(0.1О)]с = 32 /:') Billie reorders Feed Х and Feed У. Feed Х costs $58 рег 100 lb. Feed У costs $45 рег 100 lb. The order comes to $470 for 900 lb. How much of each did she order? \J А Feed Х: 350 lb; Feed У: 550 lb А (0.10' 0.18)(х+ у)= (0.12)25 В (0.18)х + 0.1 О)у = (0.12)25 С 25(0.18 + О. О)= (О.12)х О 1О + 18 � (0.12)25 . @hanae earns $8.00 рег hour during the daytime and $9.50 рег hour in the evenings after 6 Р.М. Last week she еагпеd $314.00 for 37 hours. How many daytime and evening hours did she work? В Feed Х: 400 lb; Feed У: 500 lb А 35 daytime; 2 evening О Feed Х: 500 lb; Feed У: 400 lb С 25 daytime; 12 evening С Feed Х: 450 lb; Feed У: 540 lb :.(. ·-- -.:�- 4. Alonzo needs to know how n1uch of Feed Х and Feed У to mix to get 25 lb of а mtxture that is 12% protein. Which eqll tion сап Ье used as part of а systen1 of equ tions to find tl1e solution? В 30 daytime; 7 evening D 20 daytime; 17 evening 11. а. 102 Ь.96 LESSON 3-2 / R�\�; 5х � 5 1- ; х= 3; у= 2(3) 1; (3, z 2. y+2;� ·_v,=-1;x= -1+2=1;( -1) & 3. 6; 3; х ; (2, � /_ � _ 4; 4. 8х - - 8, -1,. у � 1, 4) Challeng/ 1. у= -Зх + 22 2. у= + 6 4. у= -2. 3. �=Зх - 14 5. у= -8х 6. у= х2 - 2х . у=х2 - 4х + 8 РгоЫеm Solving _ О.18х+О.10у 1 а. {х +у= 50 + = (О.15)50 Ь. 31.25 lb of Feed Х and 18.75 lb of Feed У 2 _ а. 0.18x+(0.10)(15) = (0.12)z {x+15 = z Ь. 5 lb of Feed Х с. 20 lb of the mixtшe 3. А rs.o Reaa1ng Si:rateg1es 4. В 6.9 �ossiЫe answeг: substitution because са easily solve the first e3мation for у � 2. Possi J"\. answer: elimi9.a1ion because сап elin11�te х �г��fle system Ьу ations together adding the two / . 3. PossiЫe ans�;,: substitution becausE L сап easily s.ek, tA�econd equation for x ../ .� 4. Possible ansv11er: elimination because сап e'liminate у from the sj's m Ьу .t; n1t/tiplying the second equatюn Ьу 2, )ien adding the equations Practice А 1. а. х=4 Ь. у= 1 С.(4, 1) 2. (3, 2) 4. (-1, -3) -12х+15у=-21 5. а. { 12х - 16у=24 Ь. у=-3 с.(-2, -3) 6. (4, -1) 8. (-1, 2) Practice В 1. (10, 2) 3. (-4, -8) 5. (6, -3) 7. (8, 5) 9. (2, -3) 11. (-12, 9) d=8.25 - 8h 13. а. { 3. (1, 5) ifa� 7. (-3, 3) 2. (-3, -4) 4. (-5, 1) 6. (-3, -2) 8. (-1, 7) 10.(16,-2) 12. (-3, -7) d =3h Ь. 0.75 h ог 45 min Practice С 1. (-1.2, 4) 2. (-3, - 3 ) i 5. (-6, 11) 6. (7, 3 �) 7. (6, 7 i) 9. (9, �) 4п + 2r=23.5 1О. а. { 2n+4r=18.5 Ь. $7.00 4. (-8i,1)