Question

How do you determine whether the given ordered pair (2, -3) is a solution of the system `x=2y+8` and `2x+y=1`?

Answer 1

Just put the values of 'x' and 'y' in both of the equations and see if L.H.S and R.H.S are coming equal in each case.

This is how we do it:
`x=2y+8` (equation 1)
Putting the value of x and y in the equation
`2=2*-3+8`
`2=-6+8`
`2=2` (LHS=RHS)

For equation 2
`2x+y=1`
putting the value of x and y in the equation
`2*2+-3=1`
`4-3=1`
`1=1` (LHS=RHS)
Hence verified.

Answer 2

By substitution.

Explanation:

Ordered pair (x,y) = (2,-3) . x=2 y=-3
x=2y+8 ---> 2=2(-3)+8 ----> 2=-6+8 -> 2=2
2x+y=1 -> 2(2)+-3=1 --> 4+-3=1 --> 1=1

Note that an ordered pair is a solution of the system if it satisfy the given equation.