Question 1204546
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Given info
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 Studio A                            Studio B
classes|cost                       Classes|cost
3        70                          4     80
7        130                         6     120
8        145                         9     180
12       205                         11    220
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x = number of classes
y = total cost


Two ordered pairs with studio A are: (3,70) and (7,130)


Let's use the slope formula on those points.
{{{matrix(1,15,"Given","points:","(",x[1],",",y[1],") = ","(3,70)","and","(",x[2],",",y[2],") = ","(7,130)")}}}


{{{m = slope = rise/run = matrix(1,3,"change","in","y")/matrix(1,3,"change","in","x")}}}


{{{m = (y[2] - y[1])/(x[2] - x[1])}}}


{{{m = (130 - 70)/(7 - 3)}}}


{{{m = (60)/(4)}}}


{{{m = 15}}}
The slope 15 means the cost goes up $15 each time you take a new class. 
In other words, studio A charges $15 per class. This is on top of the $25 mat fee.
We arrive at the equation {{{y = 15x+25}}}
As a check, plug in x = 3 and you should get the result y = 70. I'll let the student do this confirmation and check the other values as well.


Follow similar steps for studio B and you should get  {{{y = 20x}}}



The system of equations is therefore
{{{system(y = 15x+25, y = 20x)}}}
x = number of classes
y = total cost
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