Quick 1. graph f(x)=2x+1 and g(x)=−x+7 on the same coordinate plane. what is the solution to the equation f(x)=g(x) ? 2. let f(x)=x+2f(x)=x+2 and g(x)=2x+1 . graph the functions on the same coordinate plane. what are the solutions to the equation f(x)=g(x) ? enter your answers in the boxes. x = or x =

1.You have two ways for solving this.
First, you could use a graphing utility or calculator to graph both functions on the same plane, and given that the functions do not have a  coordinate, the solution of  will be the  coordinate in which the tow graphs intercept (cross each other) as you can see in the picture (1).
The other way is equating the two equations and solve for x:
We know that  and , so  is equivalent to . The only thing left is solving the equation for x:



As you can see, both ways gives us the same  the solution to the equation  is .

2. For this one we can repeat the exact same procedures as before: 
Graph the functions on the same plane using a graph calculator or graphing utility, and identify the  coordinate in which the two graphs intercept as you can see in the picture (2), or you we can also equate both equations, and solve for :


And just like before, both ways gives us the same  the solution to the equation  is 

So, the answer that you should enter in your boxes are: 2 in the first, and 1 in the second one.

No solution : there is no number of boxes that she bought