Chapter 3 - Linear Systems - 3-2 Solving Systems Algebraically - Practice and Problem-Solving Exercises - Page 146: 23

$x = 2$, $y = 4$, or $(2,4)$

Given: $x + 2y = 10$ $x + y = 6$ Subtract the second equation, $x + y = 6$, from the first equation, $x + 2y = 10$. $x + 2y - (x + y) = 10 - (6)$ $x - x + 2y - y = 10 - 6$ $y = 4$ Substitute, $y = 4$ back into the first equation, $x + 2y = 10$: $x + 2y = 10$ $x + 2(4) = 10$ $x + 8 = 10$ Subtract $8$ from both sides: $x = 2$ Thus, $x = 2$, $y = 4$