Question

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

Answer 1

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

Explanation:

The equations are $y=-\frac{2}{5} x-2$ and $y=5 x+1$

Equating these two equations, we have,

$-\frac{2}{5} x-2=5 x+1$

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

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

Simplifying , we get,

$\begin{aligned}-10-5 &=25 x+2 \\-15 &=27 x \\-\frac{15}{27} &=x \\-\frac{5}{9} &=x\end{aligned}$

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

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

Thus, the solution is $\left(-\frac{5}{9},-\frac{16}{9}\right)$

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.