Hi there!
We will use x to represent children's tickets and y to represent adult tickets. Our equations would be:
x + y = 2200
1.50x + 4y = 5050
Next, we'll solve the system using substitution.
WORK:
y = 2200 - x
1.5x + 4(2200 - x) = 5050
1.5x - 4x + 8800 = 5050
-2.5x = -3750
x = 1500 children's tickets
Now, we can use the value of x to find the value of y, again using substitution.
WORK:
1(1500) + y = 2200
y = 700 adult tickets
In order to graph the system, we'll need to change both equations into slope-intercept form.
WORK:
Our regular equations are:
x + y = 2200 and 1.5x + 4y = 5050
Here are the equations in slope intercept form:
y = -x + 2200 and y = -1.5x/4 + 1262.5
Please refer to the image attached for the graph
As you can see, since the lines intersect, the solution we have come up with is correct. But here is how you would check your solution.
WORK:
x = 1500
y = 700
Plug these numbers into both equations
1500 + 700 = 2200
2200 = 2200
1.5(1500) + 4(700) = 5050
5050 = 5050
Hope this helps!! :)
If there's anything else that I can help you with, please let me know!
