Arianna and her children went into a restaurant and she bought $44 worth of hamburgers and drinks. Each hamburger costs $5.50 and each drink costs $2.75. She bought 4 more drinks than hamburgers. Graphically solve a system of equations in order to determine the number of hamburgers, x, commax, and the number of drinks, y, commay, that Arianna bought.
what are the coordinates
In order to solve this problem graphically, we can set up two equations to represent the given information.
Let x represent the number of hamburgers and y represent the number of drinks Arianna bought.
From the information given, we know that the cost of hamburgers is $5.50 and the cost of drinks is $2.75. We also know that Arianna bought 4 more drinks than hamburgers.
Equation 1: The total cost of hamburgers and drinks is $44.
5.50x + 2.75y = 44
Equation 2: The number of drinks bought is 4 more than the number of hamburgers.
y = x + 4
To graphically solve this system of equations, we can plot the two equations on a graph and find the point of intersection.
Graph:
1. Plot the y-intercepts of both equations.
- For Equation 1, let x = 0. y = 44/2.75 = 16
- For Equation 2, let x = 0. y = 0 + 4 = 4
Our two y-intercepts are (0, 16) and (0, 4).
2. Plot the x-intercepts of both equations.
- For Equation 1, let y = 0. x = 44/5.50 = 8
- For Equation 2, let y = 0. x = 0 + 4 = 4
Our two x-intercepts are (8, 0) and (4, 0).
3. Draw a line passing through the two points for each equation.
The point of intersection represents the solution to the system of equations. In this case, it represents the number of hamburgers (x) and the number of drinks (y) that Arianna bought.
Unfortunately, without values for x and y, we cannot determine the exact coordinates for the intersection point. The graph will provide an estimate or range of possible values for x and y.