Answer:
[tex] (1, -7) [/tex]
Step-by-step explanation:
To solve the system of equations by substitution, we can set the expressions for [tex] y [/tex] equal to each other:
[tex]\begin{cases} y = 7x - 14 \\y = -7x \end{cases}[/tex]
Since both expressions equal [tex] y [/tex], we can set them equal to each other:
[tex] 7x - 14 = -7x [/tex]
Now, solve for [tex] x [/tex]:
[tex] 7x + 7x = 14 [/tex]
Combine like terms:
[tex] 14x = 14 [/tex]
Divide by 14:
[tex] x = \dfrac{14}{14}[/tex]
[tex] x = 1 [/tex]
Now that we have found [tex] x = 1 [/tex], substitute it back into one of the original equations to find [tex] y [/tex]. Let's use the first equation:
[tex] y = 7(1) - 14 [/tex]
[tex] y = 7 - 14 [/tex]
[tex] y = -7 [/tex]
So, the solution to the system of equations is [tex] (1, -7) [/tex].
