Sustavi linearnih jednadžbi

Linearne jednadžbe 1

(1) Riješite sustav jednadžbi metodom supstitucije: (a) \( \text{§§V1(2,10,1)§§}x + \text{§§V2(2,10,1)§§}y = \text{§§V3(-5,5,1)§§} \) \( y = \text{§§V4(-5,-1,1)§§} \) (b) \( \text{§§V5(2,10,1)§§}x - \text{§§V6(2,10,1)§§}y = \text{§§V7(-5,5,1)§§} \) \( x = \text{§§V8(1,5,1)§§} \) (c) \( x - \text{§§V9(2,10,1)§§}y = \text{§§V10(-10,-1,1)§§} \) \( x + \text{§§V11(2,10,1)§§}y = \text{§§V12(1,10,1)§§} \) (d) \( \text{§§V13(2,10,1)§§}x + y = \text{§§V14(-10,10,1)§§} \) \( \text{§§V15(2,10,1)§§}x + y = \text{§§V16(-5,5,1)§§} \) (2) Riješite sustav jednadžbi metodom zbrajanja: (a) \( \text{§§V17(2,10,1)§§}x - \text{§§V18(2,10,1)§§}y = \text{§§V19(1,10,1)§§} \) \( \text{§§V20(-10,-2,1)§§}x + \text{§§V21(2,10,1)§§}y = \text{§§V22(1,10,1)§§} \) (b) \( \text{§§V23(2,15,1)§§}x - \text{§§V24(2,15,1)§§}y = \text{§§V25(10,40,1)§§} \) \( \text{§§V26(2,10,1)§§}x + \text{§§V27(2,15,1)§§}y = \text{§§V28(-10,-1,1)§§} \) (c) \( \text{§§V29(2,10,1)§§}x - \text{§§V30(2,10,1)§§}y = \text{§§V31(-5,5,1)§§} \) \( \text{§§V32(2,10,1)§§}y = \text{§§V33(-20,-5,1)§§} \) (d) \( \text{§§V34(-10,-2,1)§§}x + \text{§§V35(2,10,1)§§}y = \text{§§V36(1,10,1)§§} \) \( \text{§§V37(2,10,1)§§}x = \text{§§V38(5,15,1)§§} \) (e) \( \text{§§V39(2,10,1)§§}x + y = \text{§§V40(5,15,1)§§} \) \( \text{§§V41(2,10,1)§§}x - y = \text{§§V42(1,10,1)§§} \) (f) \( \text{§§V43(2,10,1)§§}x - \text{§§V44(2,10,1)§§}y = \text{§§V45(1,10,1)§§} \) \( \text{§§V46(2,10,1)§§}x + \text{§§V47(2,10,1)§§}y = \text{§§V48(1,10,1)§§} \) (g) \( \text{§§V49(2,10,1)§§}x - \text{§§V50(2,10,1)§§}y = \text{§§V51(10,30,1)§§} \) \( \text{§§V52(2,10,1)§§}x + \text{§§V53(2,10,1)§§}y = \text{§§V54(10,25,1)§§} \) (h) \( \text{§§V55(2,10,1)§§}x + \text{§§V56(2,15,1)§§}y = \text{§§V57(10,20,1)§§} \) \( \text{§§V58(5,15,1)§§}x - \text{§§V59(2,15,1)§§}y = \text{§§V60(1,10,1)§§} \) (3) Pomnožite jednu od jednadžbi sustava s §§V34(-10,-2,1)§§ i riješite sustav metodom zbrajanja: (a) \( \text{§§V61(2,10,1)§§}x + y = \text{§§V62(-15,-5,1)§§} \) \( \text{§§V63(2,10,1)§§}x + y = \text{§§V64(1,10,1)§§} \) (b) \( x + \text{§§V65(2,10,1)§§}y = \text{§§V66(1,10,1)§§} \) \( \text{§§V67(2,10,1)§§}x + \text{§§V68(2,10,1)§§}y = \text{§§V69(1,10,1)§§} \) (c) \( \text{§§V70(-10,-2,1)§§}x + \text{§§V71(2,10,1)§§}y = \text{§§V72(1,10,1)§§} \) \( \text{§§V73(2,10,1)§§}x + \text{§§V74(2,10,1)§§}y = \text{§§V75(50,100,1)§§} \) (d) \( x + \text{§§V76(2,10,1)§§}y = \text{§§V77(-30,-10,1)§§} \) \( \text{§§V78(2,10,1)§§}x + \text{§§V79(2,10,1)§§}y = \text{§§V80(-10,-1,1)§§} \) (4) Odredite kojim brojem je prikladno pomnožiti jednu od jednadžbi sustava i riješite sustav metodom zbrajanja: (a) \( \text{§§V81(2,10,1)§§}x + \text{§§V82(2,10,1)§§}y = \text{§§V83(10,30,1)§§} \) \( \text{§§V84(2,10,1)§§}x - y = \text{§§V85(1,10,1)§§} \) (b) \( \text{§§V86(2,10,1)§§}x + y = \text{§§V87(1,10,1)§§} \) \( \text{§§V88(2,10,1)§§}x - \text{§§V89(2,10,1)§§}y = \text{§§V90(-20,-5,1)§§} \)