Question

Ayuda con mates por favor

Answer 1

a)
`x = -1` and
`y = 5`, b)
`x = 2` and
`y = -1`, c)
`x = -2` and
`y = 1`, d)
`x = 2` and
`y = -9`, e)
`x = 2` and
`y = -2`, f)
`x = 2` and
`y = -1`, g)
`x = 2` and
`y = -1`, h)
`x = 1` and
`y = 2`.

Explanation:

Each system is solved as follows (Cada sistema es resuelto como sigue):

a)
`2\cdot x + y = 3` and
`3\cdot x - y = -8`

`y = 3 - 2\cdot x`

`3\cdot x - 3 + 2\cdot x = -8`

`5\cdot x = -5`

`x = -1`

`y = 5`

b)
`x - 2\cdot y = 4` and
`-x+3\cdot y = -5`

`x = 4 + 2\cdot y`

`-4-2\cdot y+3\cdot y = - 5`

`-4+y = -5`

`y = -1`

`x = 2`

c)
`-2\cdot x + 5\cdot y = 9` and
`x - y = -3`

`x = y-3`

`-2\cdot y +6 +5\cdot y = 9`

`3\cdot y = 3`

`y = 1`

`x = -2`

d)
`5\cdot x - 4\cdot y = 2` and
`3\cdot x + 2\cdot y = -12`

`3\cdot x + 2\cdot y = -12`

`6\cdot x + 4\cdot y = -24`

`4\cdot y = -6\cdot x -24`

`5\cdot x +6\cdot x +24 = 2`

`11\cdot x = -22`

`x = 2`

`y = -9`

e)
`x + y = 0` and
`2\cdot x +3\cdot y = -2`

`y = -x`

`2\cdot x -3\cdot x = -2`

`-x = -2`

`x = 2`

`y = -2`

f)
`3\cdot x + 5\cdot y = 1` and
`x + y = 1`

`y = 1 - x`

`3\cdot x + 5 - 5\cdot x = 1`

`-2\cdot x = -4`

`x = 2`

`y = -1`

g)
`5\cdot x - 2\cdot y = 12` and
`4\cdot x + 3\cdot y = 5`

`x = (12+2\cdot y)/(5)`

`x = (5-3\cdot y)/(4)`

`(12+2\cdot y)/(5) = (5-3\cdot y)/(4)`

`4\cdot (12+2\cdot y) = 5\cdot (5-3\cdot y)`

`48 + 8\cdot y = 25 - 15\cdot y`

`23\cdot y = -23`

`y = -1`

`x = 2`

h)
`7\cdot x + 8\cdot y = 23` and
`3\cdot x + 2\cdot y = 7`

`3\cdot x + 2\cdot y = 7`

`12\cdot x + 8\cdot y = 28`

`8\cdot y = 28 - 12\cdot x`

`7\cdot x +28-12\cdot x = 23`

`-5\cdot x = -5`

`x = 1`

`y = 2`