Answer:
The solutions to the system of equations are:
![x=\frac{325}{9},\:y=\frac{65}{9}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B325%7D%7B9%7D%2C%5C%3Ay%3D%5Cfrac%7B65%7D%7B9%7D)
Step-by-step explanation:
Given the system of the equations
![\begin{bmatrix}2x-y=65\\ 5y=x\end{bmatrix}](https://tex.z-dn.net/?f=%5Cbegin%7Bbmatrix%7D2x-y%3D65%5C%5C%205y%3Dx%5Cend%7Bbmatrix%7D)
isolate 'x' for 2x-y
![2x-y=65](https://tex.z-dn.net/?f=2x-y%3D65)
Add y to both sides
![2x-y+y=65+y](https://tex.z-dn.net/?f=2x-y%2By%3D65%2By)
![2x=65+y](https://tex.z-dn.net/?f=2x%3D65%2By)
Divide both sides by 2
![\frac{2x}{2}=\frac{65}{2}+\frac{y}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B2x%7D%7B2%7D%3D%5Cfrac%7B65%7D%7B2%7D%2B%5Cfrac%7By%7D%7B2%7D)
![x=\frac{65+y}{2}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B65%2By%7D%7B2%7D)
![\mathrm{Subsititute\:}x=\frac{65+y}{2}](https://tex.z-dn.net/?f=%5Cmathrm%7BSubsititute%5C%3A%7Dx%3D%5Cfrac%7B65%2By%7D%7B2%7D)
isolate 'y' for ![5y=\frac{65+y}{2}](https://tex.z-dn.net/?f=5y%3D%5Cfrac%7B65%2By%7D%7B2%7D)
![5y=\frac{65+y}{2}](https://tex.z-dn.net/?f=5y%3D%5Cfrac%7B65%2By%7D%7B2%7D)
![10y=65+y](https://tex.z-dn.net/?f=10y%3D65%2By)
subtract y from both sides
![10y-y=65+y-y](https://tex.z-dn.net/?f=10y-y%3D65%2By-y)
![9y=65](https://tex.z-dn.net/?f=9y%3D65)
Divide both sides by 9
![\frac{9y}{9}=\frac{65}{9}](https://tex.z-dn.net/?f=%5Cfrac%7B9y%7D%7B9%7D%3D%5Cfrac%7B65%7D%7B9%7D)
![y=\frac{65}{9}](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B65%7D%7B9%7D)
![\mathrm{For\:}x=\frac{65+y}{2}](https://tex.z-dn.net/?f=%5Cmathrm%7BFor%5C%3A%7Dx%3D%5Cfrac%7B65%2By%7D%7B2%7D)
![\mathrm{Subsititute\:}y=\frac{65}{9}](https://tex.z-dn.net/?f=%5Cmathrm%7BSubsititute%5C%3A%7Dy%3D%5Cfrac%7B65%7D%7B9%7D)
![x=\frac{65+\frac{65}{9}}{2}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B65%2B%5Cfrac%7B65%7D%7B9%7D%7D%7B2%7D)
![x=\frac{325}{9}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B325%7D%7B9%7D)
The solutions to the system of equations are:
![x=\frac{325}{9},\:y=\frac{65}{9}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B325%7D%7B9%7D%2C%5C%3Ay%3D%5Cfrac%7B65%7D%7B9%7D)
Answer:
2)The sum of the squares of the lengths of the legs of a right triangle is equal to the square of the length of the hypotenuse.
Step-by-step explanation:
(leg₁)² + (leg₂)² = (hypotenuse)²
Answer:The perimeter of the combined figure can be calculated by doing the sum of all sides of all figures.
Step-by-step explanation:
Answer:
9
Step-by-step explanation:
3/4 = x/12
Cross-multiply: 36 = 4x
x = 9
Answer:
y = -15
Step-by-step explanation:
x-5y=-15x−5
Let x = -5
-5 -5y = -15 * -5 -5
Combine like terms
-5 -5y = 75-5
-5 -5y = 70
Add 5 to each side
-5y = 75
Divide by -5
y = -15