Amy B. answered • 11/04/19
Amy the Mathlete
I'm going to assume the cheesecakes are French and chocolate (not marble)? If so...
This problem is tough to graph because the first equation isn't going to graph nicely with integers in slope-intercept form. Because of that, let's solve the equation first and then graph them.
Given x = the number of French cheesecakes and y = the number of chocolate cheesecakes your two equations would be
7x + 10y = 316
5x + 5y = 185
If you use multiplication to change the second equation, you can use elimination to solve.
7x + 10y = 316
-10x - 10y = -370 (<-- the original has been multiplied by -2)
-3x = -54 <-- add the equations together and the y values cancel out
/-3 /-3
x = 18.
There are 18 French cheesecakes and if you use substitution 5(18) + 5y = 185, you can see that there are then 19 chocolate cheesecakes.
This means the point (18, 19) must be the point of intersection for your two lines.
Let's stop here and get to graphing.
The second equation is easy to graph by transforming into slope-intercept form so we'll do that first.
5x + 5y = 185
-5x -5x
5y = -5x + 185
/5 /5 /5
y = -1x + 37
To graph this you will start on the y-axis at 37, and then add points using the slope (down 1, right 1)
Now, when you go to manipulate the first equation it gets pretty messy.
7x + 10y = 316
-7x -7x
10y = -7x + 316
/10 /10 /10
y = (-7/10)x + 31.6
Instead of trying to estimate 31.6 it's probably easier to just use the slope from the point we already have (18, 19). From here you can get points going either direction. If you begin at (18, 19) create additional points by moving down 7, right 10 (-7/10). Then create even more points by moving up 7 and left 10 (7/-10)
I hope this method makes graphing easier.
Let me know if you have any questions!
