1. What is the $x$-value of the solution to the system: $3x + y = 14$ and $x - y = 2$?
2. Tickets to a high school play cost $12 for adults and $8 for children. On opening night, 150 tickets were sold and total revenue was $1,440. How many more children's tickets were sold than adult tickets?
3. A taxi charges a $\$3$ flat fee plus $\$2$ per mile. Another taxi charges a $\$1$ flat fee plus $\$3$ per mile. For what number of miles $x$ do the two taxis cost the same (in dollars)?
$$\begin{cases}
y = 2x + 3\\
y = 3x + 1
\end{cases}$$
4. If $4x + y = 10$ and $2x - y = 2$, what is the value of $x$?
5. If $2x + 3y = 13$ and $2x - 3y = 1$, what is the value of $y$?
6. Solve the system of equations:
$$\begin{cases}
5x - y = 14\\
2x + y = 7
\end{cases}$$
What is the solution $(x, y)$?
7. Two numbers have sum 13 and difference 5. If $x+y=13$ and $x-y=5$, what is $(x,y)$?
8. What is the solution $(x, y)$ to the system $x + y = 9$ and $x - y = 1$?
9. If the system below is true, what is the value of $y$?
$$\begin{cases}
3x + 4y = 1\\
6x - 4y = 11
\end{cases}$$
10. Solve the system of equations:
$$\begin{cases}
2x + y = 11\\
x - y = 1
\end{cases}$$
What is the solution $(x, y)$?
11. Solve the system:
$$\begin{cases}
x + 2y = 10\\
3x - 2y = 6
\end{cases}$$
Which ordered pair satisfies both equations?
12. Consider the system of equations below: $3x + 2y = 12$ and $y = x - 4$. What is the value of $x + y$ for the solution to this system?
13. Consider the system of linear equations: $3x - y = 11$ and $2x + y = 9$. What is the value of $x$ in the solution to this system?
14. At a school store, 2 notebooks and 3 pens cost $\$12$, and 1 notebook and 2 pens cost $\$7$. If $x$ is the cost of a notebook and $y$ is the cost of a pen, what is $(x,y)$?
15. If $2x+3y=17$ and $x-y=1$, what is $x$?
16. What is the solution $(x, y)$ to the system $x + y = 6$ and $2x - y = 3$?
17. Which ordered pair satisfies both equations $y = x - 2$ and $x + y = 8$?
18. Solve the system: $3x + 2y = 12$ and $x - y = 1$.
19. Solve the system: $x + y = 7$ and $x - y = 3$.
20. If $x + y = 8$ and $x - y = 4$, what is the value of $x$?
21. Solve the system: $$\begin{cases}2x+y=11\\x-y=1\end{cases}$$ What is the solution $(x, y)$?
22. For what value of $k$, if any, does the system of equations below have no solution?$$2x + 3y = 66x + ky = 7$$
23. Solve the system:
$$\begin{cases}
x + y = 8\\
3x - y = 4
\end{cases}$$
What is the solution $(x, y)$?
24. Solve the system:
$$\begin{cases} 4x + y = 9 \\ 2x - y = 3 \end{cases}$$
Which ordered pair satisfies both equations?
25. Solve the system of linear equations:
$$\begin{cases} 2x + y = 11 \\ x - y = 1 \end{cases}$$
What is the solution $ (x, y) $?
26. Solve the system of equations:
$$\begin{cases}
5x + y = 2\\
3x - y = 14
\end{cases}$$
What is the solution $(x, y)$?
27. Solve the system:
$$\begin{cases}
4x - y = 9\\
2x + y = 3
\end{cases}$$
Which ordered pair satisfies both equations?
28. What is the solution $(x, y)$ to the system $x + y = 10$ and $x - y = 2$?
29. A taxi charges a flat fee plus a per-mile rate. A 4-mile ride costs $\$14$ and a 7-mile ride costs $\$20$. If $x$ is the flat fee and $y$ is the cost per mile, what is $(x,y)$?
30. If $4x + 2y = 18$ and $2x - y = 1$, what is the value of $y$?
31. Solve the system:
$$\begin{cases}
2x + y = 11\\
x - y = 1
\end{cases}$$
What is the solution $(x, y)$?
32. Consider the system of equations below: $3x + 2y = 12$ and $y = x - 4$. What is the value of $x + y$ for the solution to this system?