Xochitl is going to a carnival that has games and rides. Each game costs $2.50 and each ride costs $5. Xochitl spent $30 altogether on 9 games and rides. Graphically solve a system of equations in order to determine the number of games Xochitl played, x, the number of rides Xochitl went on, y.
graph coordinates
To solve this system of equations graphically, we can draw a graph representing the cost of games and rides.
Let's let the x-axis represent the number of games played (x) and the y-axis represent the number of rides taken (y).
Each game costs $2.50, so the cost of games can be represented by the equation:
2.50x
Each ride costs $5, so the cost of rides can be represented by the equation:
5y
The total amount spent, $30, can be represented by the equation:
2.50x + 5y = 30
Now, we can draw the graph by plotting points on the x and y axes. We can choose any two points to plot, and then draw a line connecting them. Let's choose (0,6) and (12,0).
To plot (0,6), we can mark 0 on the x-axis and 6 on the y-axis. This point represents 6 rides and 0 games (since 5y = 30, y = 6 and x = 0).
To plot (12,0), we can mark 12 on the x-axis and 0 on the y-axis. This point represents 0 rides and 12 games (since 2.50x = 30, x = 12 and y = 0).
Now, we can draw a line connecting these two points. The point where the line intersects the x-axis represents the number of games played (x), and the point where the line intersects the y-axis represents the number of rides taken (y).
Therefore, the solution to this system of equations is:
x = 12 games
y = 6 rides
David went to the grocery store and bought bottles of soda and bottles of juice. Each bottle of soda has 50 grams of sugar and each bottle of juice has 25 grams of sugar. David purchased a total of 14 bottles of juice and soda which collectively contain 500 grams of sugar. Graphically solve a system of equations in order to determine the number of bottles of soda purchased, x, commax, and the number of bottles of juice purchased, yy.
give my all intercepting lines and equations
To solve this system of equations graphically, we can draw a graph representing the number of bottles of soda (x) and the number of bottles of juice (y).
Let's let the x-axis represent the number of bottles of soda and the y-axis represent the number of bottles of juice.
Each bottle of soda has 50 grams of sugar, so the total grams of sugar from soda can be represented by the equation:
50x
Each bottle of juice has 25 grams of sugar, so the total grams of sugar from juice can be represented by the equation:
25y
The total grams of sugar, 500, can be represented by the equation:
50x + 25y = 500
We can now find the x and y-intercepts of this equation.
To find the x-intercept, we set y = 0 in the equation 50x + 25y = 500:
50x + 25(0) = 500
50x = 500
x = 10
So, the x-intercept is (10,0), which means 10 bottles of soda were purchased.
To find the y-intercept, we set x = 0 in the equation 50x + 25y = 500:
50(0) + 25y = 500
25y = 500
y = 20
So, the y-intercept is (0,20), which means 20 bottles of juice were purchased.
Now, we can plot these two points on the graph and draw a line connecting them. The point where the line intersects the x-axis represents the number of bottles of soda purchased (x), and the point where the line intersects the y-axis represents the number of bottles of juice purchased (y).
Therefore, the solution to this system of equations is:
x = 10 bottles of soda
y = 20 bottles of juice
can you graph the intercepting lines for (10,20)
Apologies for the confusion earlier. Since the given solution is (10,20), which means 10 bottles of soda and 20 bottles of juice were purchased, we don't need to find intercepts in this case. We can directly plot the point (10,20) on the graph.
On the x-axis, mark the point 10, and on the y-axis, mark the point 20. These two points represent the number of bottles of soda (x=10) and the number of bottles of juice (y=20).
Now we can mark this point (10,20) on the graph.
To graphically solve a system of equations, you will need to plot the equations on a coordinate plane, where the x-axis represents the number of games played (x), and the y-axis represents the number of rides taken (y). Each point on the coordinate plane represents a possible solution to the system of equations.
Let's denote the number of games played by x and the number of rides taken by y.
From the given information, we know that each game costs $2.50 and each ride costs $5, and Xochitl spent a total of $30. This can be expressed mathematically by the following equations:
Equation 1: 2.50x + 5y = 30 (represents the total cost of games and rides)
Equation 2: x + y = 9 (represents the total number of games and rides)
To graphically solve this system of equations:
1. Plot the y-intercept: To find the y-intercept of Equation 2, set x = 0 and solve for y. In this case, y = 9. Plot the point (0, 9) on the coordinate plane.
2. Plot additional points: To plot additional points, you can choose any other value for x in Equation 2 and solve for y. For example, if you choose x = 3, you can solve Equation 2 for y to find y = 6. Plot the point (3, 6) on the coordinate plane.
3. Connect the points: Once you have plotted a few points, connect them to create a line. This line represents the solutions to Equation 2.
4. Find the point of intersection: Plot the line represented by Equation 1 on the same coordinate plane. The point where the two lines intersect represents the solution to the system of equations.
To find the coordinates of the point of intersection, you can solve the system of equations algebraically by substitution or elimination methods.