So I attempted this and I'm not sure if it's the correct answer - and I don't know how to graph it..
Student tickets to the Homecoming game cost $5 each. General admission tickets cost $8 each. So far, 150 tickets have been sold. $900 has been collected.
A. Write a system of equations for this model in standard form.
Equation 1: g+s=150
Equation 2: 8g +5s = 900
B. Graph the system. (let each square represent 20 units)
C. What is the solution to the system?
(this is my attempt)
G = 150 – s
8(150-s)+5s=900
1200-8s+5s=900
-900 -900
300/3-3s/3
Answer:
100=student tickets and 50=general admission tickets
And I don't know how to check this one, or atleast how to plug it in, /to/ check it:
D.Is (180, -30) a solution? Explain.
your solution is correct.
To check on (180,-30), plug it in
8(180)+5(-30) =?= 900
But, how do you sell -30 student tickets?
To graph the system of equations, you can use the slope-intercept form of equations (y = mx + b) by solving each equation for one variable in terms of the other.
For Equation 1: g + s = 150
You can rewrite it as s = 150 - g by subtracting g from both sides.
For Equation 2: 8g + 5s = 900
You can solve it for s by subtracting 8g from both sides and then dividing by 5:
s = (900 - 8g) / 5
To graph this system of equations, you plot points on a coordinate plane where the x-axis represents the number of general admission tickets (g) and the y-axis represents the number of student tickets (s). Each square on the graph will represent 20 units.
Start by substituting different x (g) values into the equation for s and then plot the corresponding points. For example, if g = 0, s = 150 - 0 = 150. So you would plot the point (0, 150). Repeat this process for a few more values of g to get multiple points.
Once you have a few points, you can connect them with a straight line to visualize the relationship between the variables.
To check if the solution (100, 50) is correct, you can substitute these values into the equations and see if they satisfy both equations:
For Equation 1: g + s = 150
Substituting g = 100 and s = 50: 100 + 50 = 150 (which is true)
For Equation 2: 8g + 5s = 900
Substituting g = 100 and s = 50: 8(100) + 5(50) = 900 (which is true)
So, (100, 50) is a valid solution to the system of equations.
To check if (180, -30) is a solution, substitute these values into the equations:
For Equation 1: g + s = 150
Substituting g = 180 and s = -30: 180 + (-30) = 150 (which is false)
Since (180, -30) does not satisfy Equation 1, it is not a solution to the system.