Given that the solution of the system of equations x-2y = 0, BX + ay = 2 is the same as that of the system of equations 2x + y = 5, ax + ay = 1, find the value of a and B

Given that the solution of the system of equations x-2y = 0, BX + ay = 2 is the same as that of the system of equations 2x + y = 5, ax + ay = 1, find the value of a and B

The solutions of the two equations are the same, which means that X and y satisfy the four equations at the same time
Take two equations without a and B to solve X and Y simultaneously
x-2y=0
2x+y=5
x=2y
5y=5
y=1,x=2
Then we substitute the equation with a and B
2b+a=2
2a+a=1
3a=1
a=1/3
2b+1/3=2
2b=5/3
b=5/6
So a = 1 / 3, B = 5 / 6

Given that a system of equations x + 2Y = 10, ax + by = 1 has the same solution as the system of equations 2x-y = 5, BX + ay = 6, find the solution of the system of equations and the value of a, B

X + 2Y = 10 2x-y = 5, the solution of the two equations is
X = 4, y = 3. This is the same solution of the two equations in the original problem, which is obtained by substituting ax + by = 1 and BX + ay = 6
4a+3b=1
3A + 4B = 6, a = - 2, B = 3