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)

Question

asked Feb 10, 2021 187k views

2 Answers

Tom Carr · Answer 1 · 2021-02-15T22:20:22+0000

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.