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CAPITULO XXIV

Ecuaciones simultaneas con dos incognitas
Ejercicio 176
Resolver por el método de igualación:
  1. { x+6y=27 ( 1 ) 7x–3y=9 ( 2 ) Despejando x de ( 1 ) x =27–6y Despejando x de ( 2 ) 7x =3y+9 x = 3y+9 7 Igualando ambas ecuaciones 27–6y = 3y+9 7 7(27–6y ) =3y+9 189–42y =3y+9 –42y–3y =9–189 –45y =–180 y = – – 45 y =4 Reemplazo y en ( 1 ) x =27–6( 4 ) x =27–24 x =3 Sol.{ x=3 y=4
  2. { 3x–2y=–2 ( 1 ) 5x+8y=–60 ( 2 ) Despejando x de ( 1 ) 3x =2y–2 x = 2y–2 3 x = 2(y–1 ) 3 Despejando x de ( 2 ) 5x =–60–8y x = –60–8y 5 x =– 4(15+2y ) 5 Igualando ambas ecuaciones 2 (y–1 ) 3 =– (15+2y ) 5 5(y–1 ) =–6(15+2y ) 5y–5 =–90–12y 5y+12y =5–90 17y =–85 y = – 17 y =–5 Reemplazo y en ( 1 ) 3x =2(–5 ) –2 3x =–10–2 3x =–12 x = – 3 x =–4 Sol.{ x=–4 y=–5
  3. { 3x+5y=7 ( 1 ) 2x–y=–4 ( 2 ) Despejando x de ( 1 ) 3x =7–5y x = 7–5y 3 Despejando x de ( 2 ) 2x =y–4 x = y–4 2 Igualando ambas ecuaciones 7–5y 3 = y–4 2 2(7–5y ) =3(y–4 ) 14–10y =3y–12 –3y–10y =–14–12 –13y =–26 y = – – 13 y =2 Reemplazo y en ( 1 ) 3x =7–5( 2 ) 3x =7–10 3 x =– 3 x =–1 Sol.{ x=–1 y=2
  4. { 7x–4y=5 ( 1 ) 9x+8y=13 ( 2 ) Despejando x de ( 1 ) 7x =4y+5 x = 4y+5 7 Despejando x de ( 2 ) 9x =13–8y x = 13–8y 9 Igualando ambas ecuaciones 4y+5 7 = 13–8y 9 9(4y+5 ) =7(13–8y ) 36y+45 =91–56y 36y+56y =91–45 92y =46 y = 46 y = 1 2 Reemplazo y en ( 1 ) 7x =( 1 2 ) +5 7 x = 7 x =1 Sol.{ x=1 y= 1 2
  5. { 9x+16y=7 ( 1 ) 4y–3x=0 ( 2 ) Despejando x de ( 1 ) 9x =7–16y x = 7–16y 9 Despejando x de ( 2 ) 3x =4y x = 4y 3 Igualando ambas ecuaciones 7–16y 9 = 4y 3 3(7–16y ) =9(4y ) 21–48y =36y –48y–36y =–21 –84y =–21 y = – 21 – y = 1 4 Reemplazo y en ( 2 ) 3x =4y 3x = 4 ( 1 4 ) x = 1 3 Sol.{ x= 1 3 y= 1 4
  6. { 14x–11y=–29 ( 1 ) 13y–8x=30 ( 2 ) Despejando x de ( 1 ) 14x =11y–29 x = 11y–29 14 Despejando x de ( 2 ) –8x =30–13y x = 13y–30 8 Igualando ambas ecuaciones 11y–29 = 13y–30 4(11y–29 ) =7(13y–30 ) 44y–116 =91y–210 44y–91y =116–210 –47y =–94 y = – – 47 y =2 Reemplazo y en ( 2 ) 14x =11y–29 14x =11( 2 ) –29 14x =22–29 14x =–7 x = – 7 x =– 1 2 Sol.{ x= 1 3 y= 1 4
  7. { 15x–11y=–87 ( 1 ) –12x–5y=–27 ( 2 ) Despejando x de ( 1 ) 15x =11y–87 x = 11y–87 15 Despejando x de ( 2 ) –12x =5y–27 x =– 5y–27 12 Igualando ambas ecuaciones 11y–87 =– 5y–27 4(11y–87 ) =–5(5y–27 ) 44y–348 =–25y+135 44y+25y =348+135 69y =483 y = 69 y =3 Reemplazo y en ( 2 ) –12x =5y–27 –12x =5( 3 ) –27 –12x =15–27 – 12 x =– 12 x =1 Sol.{ x=1 y=3
  8. { 7x+9y=42 ( 1 ) 12x+10y=–4 ( 2 ) Despejando x de ( 1 ) 7x =42–9y x = 42–9y 7 Despejando x de ( 2 ) 12x =–4–10y x =– 2 (2+5y ) x =– 2+5y 6 Igualando ambas ecuaciones 42–9y 7 =– 2+5y 6 6(42–9y ) =–7(2+5y ) 252–54y =–14–35y 35y–54y =–252–14 –19y =–266 y = – – 19 y =14 Reemplazo y en ( 1 ) 7x =42–9y 7x =42–9( 14 ) 7x =42–126 7x =–84 x =– 7 x =–12 Sol.{ x=–12 y=14
  9. { 6x–18y=–85 ( 1 ) 24x–5y=–5 ( 2 ) Despejando x de ( 1 ) 6x =18y–85 x = 18y–85 6 Despejando x de ( 2 ) 24x =5y–5 x = 5y–5 24 x = 5(y–1 ) 24 Igualando ambas ecuaciones 18y–85 6 = 5(y–1 ) 4(18y–85 ) =5y–5 72y–340 =5y–5 72y–5y =340–5 67y =335 y = 67 y =5 Reemplazo y en ( 2 ) 24x =5y–5 24x =5( 5 ) –5 24x =25–5 24x =20 x = x = 5 6 Sol.{ x= 5 6 y=5
Categories: Capítulo XXIV