Question

Which ordered pair is the solution to this system of equations?

Answer 1

Answer: (-10, -1)

Step-by-step explanation:

     To solve, I will graph the given system of equations.

-> See attached.

    The solution is the point at which the lines intersect. Also known as the point of intersection.

     In this case, the point of intersection is (-10, -1) giving us our answer.

Answer 2

Answer:

A. (-10, -1)

Step-by-step explanation:

Given system of equations:

$\begin{cases}\sf x+5y=-15\\\sf y=\dfrac{1}{5}x+1\end{cases}$

Solve for x:

1. Substitute the value of y in the second equation into the first equation:

$\sf x+5\left(\dfrac{1}{5}x+1\right)=-15$

2. Distribute 5 through the parentheses:

$\sf x+5\left(\dfrac{1}{5}x\right)+5(1)=-15\\\\\Rightarrow x+x+5=-15\ \textsf{[ combine like terms ]}\\\\\Rightarrow 2x+5=-15$

3. Subtract 5 from both sides:

$\sf 2x+5-5=-15-5\\\\\Rightarrow 2x=-20$

4. Divide both sides by 2

$\sf \dfrac{2x}{2}=\dfrac{-20}{2}\\\\\Rightarrow \boxed{\sf x=-10}$

Solve for y:

5. Substitute the found x-value (-5) into one of the given equations:

$\sf x+5y=-15\\\\\Rightarrow -10+5y=-15$

6. Add 10 to both sides:

$\sf -10+10+5y=-15+10\\\\\Rightarrow 5y=-5$

7. Divide both sides by 5:

$\sf \dfrac{5y}{5}=\dfrac{-5}{5}\\\\\Rightarrow \boxed{\sf y=-1}$

Coordinate: (-10, -1)

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