Question

For each ordered pair determine whether it is a solution to the system of equations 2x-7y=8 -3x+2y=5

Answers:
(-3,-2)

(4,0)

(5,4)

(-7,-8)

Answer 1

The solution of this system of linear equations is
`(x,y) = (-3,-2)`.

Explanation:

Let be the following system of linear equations:

`2\cdot x - 7\cdot y = 8` (1)

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

From (1) we clear
`y`:

`2\cdot x -8 = 7\cdot y`

`y = (2\cdot x - 8)/(7)`

And we apply this variable in (2):

`-3\cdot x+2\cdot \left((2\cdot x -8)/(7) \right)= 5`

`-3\cdot x +(4)/(7) \cdot x -(16)/(7) = 5`

`-(17)/(7)\cdot x = (51)/(7)`

`x = -(51)/(17)`

`x = -3`

And the value of
`y` is:

`y = (2\cdot (-3)-8)/(7)`

`y = -(14)/(7)`

`y = -2`

The solution of this system of linear equations is
`(x,y) = (-3,-2)`.