Write a detailed solution to the system
x 1 3y # 9
y # 22x 1 6, where x $ 0 and y $ 0.
Graph the system to show all possible solutions.
Try using the symbols = < > and <= >=
ok0iko
To solve the given system of equations:
1. Start by solving the first equation:
x + 3y = 9
To isolate x, subtract 3y from both sides:
x = (9 - 3y)
2. Now, substitute this value of x into the second equation:
y = 22x + 6
Substitute x with (9 - 3y):
y = 22(9 - 3y) + 6
Simplify the equation:
y = 198 - 66y + 6
y + 66y = 204
67y = 204
Divide by 67 to get the value of y:
y = 3
3. Substitute the value of y back into the first equation to find the value of x:
x + 3(3) = 9
x + 9 = 9
x = 0
So, the solution to the given system is x = 0 and y = 3.
To graph the system to show all possible solutions:
1. Set up a coordinate plane with x and y axes.
2. Plot the point (0, 3) as this is the solution to the system.
3. You can also draw the lines representing the two equations:
- For the first equation, x + 3y = 9, rearrange it as y = (9 - x)/3. Plot this line on the graph.
- For the second equation, y = 22x + 6, plot this line on the graph as well.
The graph should intersect at the point (0, 3), which represents the solution to the system.