On two systems of equations of XY

On two systems of equations of XY

The first solution is x-2y = 5
3x+2y=7
Add
4x=12
x=3,y=(x-5)/2=-1
Put in the other two
3a-b=-7
3b-a=-1
a=3b+1
Substituting 3a-b = - 7
9b+3-b=-7
b=-5/4
a=3b+1=-11/4

It is known that the solution of {ax + by = - 16 CX + 20Y = - 224 is {x = 8, y = - 10, Xiao Ming copied C wrong, so the solution is: x = 12, y = - 13, then
The second power of a + the second power of B + the second power of C

X = 12, y = - 13 is the solution of equation 1, substituting it, we can see: 12a-13b = - 16
X = 8, y = - 10 are the solutions of the equations. Substitution shows that 8a-10b = - 16; 8C + 20 * (- 10) = - 224
A = 3; b = 4; C = - 3
Substituting into the formula: A ^ 2 + B ^ 2 + C ^ 2 = 9 + 16 + 9 = 34

Given the same solution of the system of equations x + y = 3, ax + by = 4 and ax-2by = 22, X-Y = 7, find the value of 3a-16

Solve the equations {x + y = 3, X-Y = 7
We get x = 5, y = - 2
Substituting the solution into ax + by = 4 and ax-2by = 22
5a-2b = 4, 5A + 4B = 22
The solution is a = 2, B = 3
So 3a-16 = 6-16 = - 10