Answer:
[tex] (-3, 1) [/tex]
Step-by-step explanation:
To solve the system of equations by substitution, we'll set the expressions for [tex] y [/tex] equal to each other:
Given:
[tex]\begin{cases} y = 2x + 7 \\ y = 7x + 22 \end{cases}[/tex]
Since both expressions equal [tex] y [/tex], we can set them equal to each other:
[tex]2x + 7 = 7x + 22[/tex]
Now, solve for [tex] x [/tex]:
[tex]2x - 7x = 22 - 7[/tex]
[tex]-5x = 15[/tex]
[tex]x = \dfrac{15}{-15}[/tex]
[tex]x = -3[/tex]
Now that we have found [tex] x = -3 [/tex], we can substitute it back into one of the original equations to find [tex] y [/tex]. Let's use the first equation:
[tex]y = 2(-3) + 7[/tex]
[tex]y = -6 + 7[/tex]
[tex]y = 1[/tex]
So, the solution to the system of equations is [tex] (-3, 1) [/tex].
