Answer:
[tex] (-2, -1) [/tex]
Step-by-step explanation:
We are given the following system of equations:
[tex] \begin{cases} y = -2x - 5 \\ -8x + 2y = 14 \end{cases} [/tex]
We can solve this system by substituting the expression for [tex] y [/tex] from the first equation into the second equation and then solving for [tex] x [/tex].
First, we substitute [tex] y = -2x - 5 [/tex] into the second equation:
[tex] -8x + 2(-2x - 5) = 14 [/tex]
Now, let's solve for [tex] x [/tex]:
[tex] -8x - 4x - 10 = 14 [/tex]
[tex] -12x - 10 = 14 [/tex]
Add 10 to both sides:
[tex] -12x = 14 + 10 [/tex]
[tex] -12x = 24 [/tex]
Now, divide by -12:
[tex] x = \dfrac{24}{-12} [/tex]
[tex] x = -2 [/tex]
Now that we have found [tex] x = -2 [/tex], we can substitute this value into the first equation to find [tex] y [/tex]:
[tex] y = -2(-2) - 5 [/tex]
[tex] y = 4 - 5 [/tex]
[tex] y = -1 [/tex]
So the solution to the system of equations is [tex] (-2, -1) [/tex].
