1. Decide whether each \((x,y)\) pair is a solution to one equation, both equations, or neither of the equations.

   1. \((3 ,4)\)
   2. \((4, 2.5)\)
   3. \((5, 5)\)
   4. \((3, 2)\)
2. Is it possible to have more than one \((x,y)\) pair that is a solution to both equations? Explain or show your reasoning. 

Explain or show that the point \((5,\text-4)\) is a solution to this system of equations: \( \begin{cases} 3x-2y=23 \\ 2x+y=6 \\ \end{cases}\)

Diego is thinking of two positive numbers. He says, “If we triple the first number and double the second number, the sum is 34.”

1. Write an equation that represents this clue. Then, find two possible pairs of numbers Diego could be thinking of.

2. Diego then says, “If we take half of the first number and double the second, the sum is 14.”

   Write an equation that could represent this description.

3. What are Diego’s two numbers? Explain or show how you know. A coordinate plane is given here, in case it's helpful.

   

Andre does not understand why a solution to the equation \(3-x=4\) must also be a solution to the equation \(12=9-3x\).

Write a convincing explanation as to why this is true.

Volunteer drivers are needed to bring 80 students to the championship baseball game. Drivers either have cars, which can seat 4 students, or vans, which can seat 6 students. The equation \(4c+6v=80\) describes the relationship between the number of cars \(c\) and number of vans \(v\) that can transport exactly 80 students.

Explain how you know that this graph represents this equation.

Graph of a line, origin O. Horizontal axis, number of cars, scale is 0 to 24, by 2’s. Vertical axis, number of vans, scale is 0 to 16, by 2’s. Line starts on the vertical axis and passes through the points 8 comma 8, 14 comma 4, and ends on the horizontal axis at 20.

Three siblings are participating in a family-friendly running event.

• The oldest sibling begins at the start line of the race and runs 7 miles per hour the entire time.
• The middle sibling begins at the start line and walks at 3.5 miles per hour throughout the race.
• The youngest sibling joins the race 4 miles from the start line and runs 5 miles per hour the rest of the way.

Match each graph to the sibling whose running is represented by the graph.

What is the \(x\)-intercept of the graph of \(y = 3 - 5x\)?