Question

Which ordered pair is the best estimate for the solution of the system of equations? y=−2/5x−2y=5x+1

(−0.5, −1.75)

(−1, −2)

(0, −2)

(−0.5, −1)

Answer 1

Answer: Answer is A

Step-by-step explanation: Took the test

Answer 2

Option a:
`(-0.5,-1.75)` is the solution to the system of equations.

Step-by-step explanation:

The equations are
`y=-(2)/(5) x-2` and
`y=5 x+1`

Equating these two equations, we have,

`-(2)/(5) x-2=5 x+1`

Taking LCM and multiplying both sides by 5, we get,

`-2 x-10=25 x+5`

Simplifying , we get,

`\begin{aligned}-10-5 &=25 x+2 \\-15 &=27 x \\-(15)/(27) &=x \\-(5)/(9) &=x\end{aligned}`

Substituting the value of x in
`y=5 x+1`, we get,

`\begin{aligned}&y=5\left(-(5)/(9)\right)+1\\&y=-(25)/(9)+1\\&y=-(16)/(9)\end{aligned}`

Thus, the solution is
`\left(-(5)/(9),-(16)/(9)\right)`

Changing the solution from fraction to decimal, we get,
`(-0.556,-1.778)`

Thus, the solution is
`(-0.5,-1.75)`

Hence, option a is the correct answer.