Power standard 7: real world problems
a local organic farmer sold 8 boxes of peaches and 6 boxes
of tomatoes to one customer for $82. a second customer
purchased 6 boxes of peaches and 7 boxes of tomatoes. she
spent $79. how much did a box of peaches and a box of
tomatoes cost? write and solve a system of equations. show
your steps.

The cost of one box of peaches is $5 and the cost of one box of tomatoes is $7

Step-by-step explanation:

Let

x ----> the cost of one box of peaches

y ---> the cost of one box of tomatoes

we know that

-----> equation A

-----> equation B

Solve the system of equations by graphing

The solution of the system of equations is the intersection point both graphs

The solution is the point (5,7)

see the attached figure

therefore

The cost of one box of peaches is $5 and the cost of one box of tomatoes is $7

for the friend request.

when a figure, such as triangle (xyz) is reflected over the line y = x to create x'y'z' the x-coordinates and y-coordinates of the original image (pre-image) will be reversed for the image. (e.g., (x, y) > (y, x)) this means that the pre-image position of the x- and y-coordinates switch places which in turn provides a mirror like image of the original xyz.  

i notice that when i draw a line segment from x to x', that the points are parallel from each other -- they are exactly across from each other and do not intersect with any other points.  

yes, think i would see the same characteristic if you drew the line segment connecting y with the reflecting line and then y' with the reflecting line because of the essence of reflections. because it is a mirror image, each point was effected the same way which leads me to conclude that they same would apply to y and y'.

yes   because as the functions are graphed they eventually will intersect unless otherwise

step-by-step explanation: