Question 1200279
Mikes repair shop: y=100+65X
Amys auto repair:Y=40+80X
the lines will intersect when 100 + 65x = 40 + 80x
subtract 65x from both sides of the equation and subtract 40 from both sides of the equation to get 60 = 15x
solve for x to get x = 60/15 = 4
when x = 4:
y = 100 + 65 * 4 = 360
y = 40 + 80 * 4 = 360
the common solution to both equations is when x = 4 and y = 360.
the interpretation is that the cost to do a repair in either mike's shop or amy's shop when the number of hours to repair the car is 4.
this is what the intersection of the two equation looks like on a graph.
<img src = "http://theo.x10hosting.com/2023/021001.jpg">