Respuestas
Primera ecuación:
4x + 9y = 1... (1)
7x - 8y = -9... (2)
Multiplicamos (1) × 8
[4x + 9y = 1] × 8
32x + 72y = 8... (3)
Multiplicamos (2) × 9
[7x - 8y = -9] × 9
63x - 72y = -81... (4)
Sumamos (3) y (4):
32x + 72y = 8... (3)
63x - 72y = -81... (4)
→ 32x + 63x = 8 - 81
95x = -73
x = -73/95
Reemplazamos en (1):
4x + 9y = 1
4(-73/95) + 9y = 1
9y = 1 - 4(-73/95)
9y = 387/95
y = (387/95)/9
y = 43/95
{x = -73/95; y = 43/95}
Segunda ecuación:
2x + 3y = -1... (1)
3x + 4y = 0... (2)
Multiplicamos (1) × 3 y (2) × -2
6x + 9y = -3
-6x -8y = 0
→ y = -3
Reemplazamos en (1):
2x + 3y = -1
2x + 3(-3) = -1
2x = -1 + 9
2x = 8
x = 4
{x = 4; y = -3}
Tercera ecuación:
2x - 3y = 7... (1)
x + 5y = 23... (2)
Multiplicamos (2) × -2
2x - 3y = 7
-2x - 10y = -46
→ -13y = -39
y = 39/13
y = 3
Reemplazamos en (1):
2x - 3y = 7
2x = 7 + 9
2x = 16
x = 8
{x = 8; y= 3}
Cuarta ecuación:
2x + 3y = -1... (1)
6x + 5y = -7... (2)
Multiplicamos (1) × -3
-6x - 9y = 3
6x + 5y = -7
→ -4y = -4
y = 1
Reemplazamos en (1):
2x + 3y = -1
2x = -1 - 3
2x = -4
x = -2
{x = -2; y = 1}
Quinta ecuación:
5x - y = 3... (1)
-2x + 4y = -12... (2)
Multiplicamos (1) × 2 y (2) × 5:
10x - 2y = 6
-10x + 20y = -60
→ 18y = -54
y = -3
Reemplazamos en (1)
5x - y = 3
5x = 3 - 3
5x = 0
x = 0
{x = 0; y = -3}
Sexta ecuación:
2x + y = 9... (1)
3x + 5y = 17... (2)
Multiplicamos (1) × -3 y (2) × 2
-6x - 3y = -27
6x + 10y = 34
→ 7y = 7
y = 1
Reemplazamos en (1):
2x + y = 9
2x = 9 - 1
2x = 8
x = 4
{x = 4; y = 1}