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Kuta Software - Infinite Algebra 2 Name___________________________________ Systems of Two Equations Date________________ Period____ Solve each system by graphing. 1) y = −3 x + 4 y = 3x − 2 −5 −4 −3 −2 2) y = x + 2 x = −3 5 5 4 4 3 3 2 2 1 1 −1 0 −1 1 2 3 4 5 −5 −3 −2 −1 0 −1 −2 −3 −3 −4 −4 −5 −5 1 2 3 4 5 1 2 3 4 5 (−3, −1) 3) x − y = 3 7 x − y = −3 −4 −3 −2 (1, 1) −5 −4 −2 4) 4 x + y = 2 x− y=3 5 5 4 4 3 3 2 2 1 1 −1 0 −1 1 2 3 4 5 −5 −4 −3 −2 −1 0 −1 −2 −2 −3 −3 −4 −4 −5 −5 (−1, −4) (1, −2) Solve each system by substitution. 5) y = 4 x − 9 y=x−3 6) 4 x + 2 y = 10 x − y = 13 (2, −1) (6, −7) 7) y = −5 5 x + 4 y = −20 (0, −5) 8) x + 7 y = 0 2 x − 8 y = 22 (7, −1) ©X I2e0s152Z XKZuOtGaI fSEoyfEtewLayrKev MLkL3CQ.L i lAWl2lV Xr4iogShBtjsh trceRsBeorVvseid5.K S TM4aPdWee KwmiptNhV UIGndf3ihnyiAt3ed HA1l9gTeNbPrSal s2S.B -1- Worksheet by Kuta Software LLC 9) 6 x + 8 y = −22 y = −5 (3, −5) 11) 7 x + 2 y = −19 − x + 2 y = 21 (−5, 8) 13) −7 x + 4 y = 24 4x − 4 y = 0 (−8, −8) Solve each system by elimination. 10) −7 x + 2 y = 18 6x + 6 y = 0 (−2, 2) 12) 3 x − 5 y = 17 y = −7 (−6, −7) 14) 4 x − y = 20 −2 x − 2 y = 10 (3, −8) 15) 8 x − 6 y = −20 −16 x + 7 y = 30 16) 6 x − 12 y = 24 −x − 6 y = 4 (−1, 2) 17) −8 x − 10 y = 24 6x + 5 y = 2 (7, −8) (2, −1) 18) −24 − 8 x = 12 y 5 7 1+ y=− x 9 18 (6, −6) 19) −4 y − 11 x = 36 20 = −10 x − 10 y 20) −9 + 5 y = −4 x −11 x = −20 + 9 y (−4, 2) 21) 0 = −2 y + 10 − 6 x 14 − 22 y = 18 x (1, 1) 22) −16 y = 22 + 6 x −11 y − 4 x = 15 (2, −1) 23) −16 + 20 x − 8 y = 0 36 = −18 y − 22 x (−1, −1) 5 11 − x = −y 7 7 2 y = 7 + 5x 24) − (0, −2) (−3, −4) Critical thinking questions: 25) Write a system of equations with the solution (4, −3). Many answers. Ex: x + y = 1, 2 x + y = 5 Create your own worksheets like this one with Infinite Algebra 2. Free trial available at KutaSoftware.com ©E h2p0Y132b CKZugtsau ZShoMfGtmwUaBrLe7 2LQLSCW.T t 5AalxlK 0rhiwgthft5sA 7rPe3ssezrQvFeZdb.9 N 7Mnazdiez nw2iRtehi JIBnwfJiwnjiktgeL 1Acl6gneYbTrtaJ v2D.O -2- Worksheet by Kuta Software LLC Kuta Software - Infinite Pre-Algebra Name___________________________________ Systems of Equations Word Problems Date________________ Period____ 1) Kristin spent $131 on shirts. Fancy shirts cost $28 and plain shirts cost $15. If she bought a total of 7 then how many of each kind did she buy? 2 fancy shirts and 5 plain shirts 2) There are 13 animals in the barn. Some are chickens and some are pigs. There are 40 legs in all. How many of each animal are there? 6 chickens and 7 pigs 3) A farmhouse shelters 10 animals. Some are pigs and some are ducks. Altogether there are 36 legs. How many of each animal are there? 2 ducks and 8 pigs 4) A class of 195 students went on a field trip. They took 7 vehicles, some cars and some buses. Find the number of cars and the number of buses they took if each car holds 5 students and each bus hold 45 students. 3 cars and 4 buses ©r D2w0I1m2i 1KAu0tfaP ESMoVfHtTw8aOrPed xLWLtCf.b U wA6ljlp IriiWgOh7tOsy QrueGsTeJrgvFeAd8.3 w BMlacdceU Ow4iSt1hv BIMnUfAi8nIi5tAeU 1PjrYeN-hAtlbgGecbZrha4.W -1- Worksheet by Kuta Software LLC