Answer:
{x,y} = {5,6}
Step-by-step explanation:
// Solve equation [1] for the variable x
[1] x = y - 1
// Plug this in for variable x in equation [2]
[2] 2•(y -1) - y = 4
[2] y = 6
// Solve equation [2] for the variable y
[2] y = 6
// By now we know this much :
x = y-1
y = 6
// Use the y value to solve for x
x = (6)-1 = 5
154
Subtract $1060 from $5680 to get $4620 > divide $4620 by $30 to get 154 > 154 students can attend
Answer:
LMN has a larger area
Step-by-step explanation:
Given
RST
![R =(5,5)](https://tex.z-dn.net/?f=R%20%3D%285%2C5%29)
![S= (2,1)](https://tex.z-dn.net/?f=S%3D%20%282%2C1%29)
![T = (1,3)](https://tex.z-dn.net/?f=T%20%3D%20%281%2C3%29)
LMN
![L = (0,-1)](https://tex.z-dn.net/?f=L%20%3D%20%280%2C-1%29)
![M= (2,-4)](https://tex.z-dn.net/?f=M%3D%20%282%2C-4%29)
![N= (-2,-3)](https://tex.z-dn.net/?f=N%3D%20%28-2%2C-3%29)
Required
Compare both areas
The area of triangle is:
![Area = \frac{1}{2}|x_1y_2 - x_2y_1 + x_2y_3 - x_3y_2 + x_3y_1 - x_1y_3|](https://tex.z-dn.net/?f=Area%20%3D%20%5Cfrac%7B1%7D%7B2%7D%7Cx_1y_2%20-%20x_2y_1%20%2B%20x_2y_3%20-%20x_3y_2%20%2B%20x_3y_1%20-%20x_1y_3%7C)
For RST, we have:
![Area = \frac{1}{2}|5*1 - 2*5 + 2*3 - 1*1 + 1*5 - 5*3|](https://tex.z-dn.net/?f=Area%20%3D%20%5Cfrac%7B1%7D%7B2%7D%7C5%2A1%20-%202%2A5%20%2B%202%2A3%20-%201%2A1%20%2B%201%2A5%20-%205%2A3%7C)
![Area = \frac{1}{2}|-10|](https://tex.z-dn.net/?f=Area%20%3D%20%5Cfrac%7B1%7D%7B2%7D%7C-10%7C)
Remove absolute signs
![Area = \frac{1}{2}*10](https://tex.z-dn.net/?f=Area%20%3D%20%5Cfrac%7B1%7D%7B2%7D%2A10)
![Area = 10](https://tex.z-dn.net/?f=Area%20%3D%2010)
For LMN, we have:
![Area = \frac{1}{2}|x_1y_2 - x_2y_1 + x_2y_3 - x_3y_2 + x_3y_1 - x_1y_3|](https://tex.z-dn.net/?f=Area%20%3D%20%5Cfrac%7B1%7D%7B2%7D%7Cx_1y_2%20-%20x_2y_1%20%2B%20x_2y_3%20-%20x_3y_2%20%2B%20x_3y_1%20-%20x_1y_3%7C)
![Area = \frac{1}{2}|0*-4-2*-1+2*-3--2*-4--2*-1-0*-3|](https://tex.z-dn.net/?f=Area%20%3D%20%5Cfrac%7B1%7D%7B2%7D%7C0%2A-4-2%2A-1%2B2%2A-3--2%2A-4--2%2A-1-0%2A-3%7C)
![Area = \frac{1}{2}|-14|](https://tex.z-dn.net/?f=Area%20%3D%20%5Cfrac%7B1%7D%7B2%7D%7C-14%7C)
Remove absolute signs
![Area = \frac{1}{2}*14](https://tex.z-dn.net/?f=Area%20%3D%20%5Cfrac%7B1%7D%7B2%7D%2A14)
![Area = 7](https://tex.z-dn.net/?f=Area%20%3D%207)
<em>By comparing both areas, we can conclude that LMN has a larger area</em>