Solving Equations

2 Examples solving a system of equations:

Solve[{a  x + y == 0 , 2   x - (1-a)  y ==1},{x,y}]

Try to replace a by 10 using the replacement operator try the exact solution and the numerical solution

Solve[{a  x + y == 0 , 2   x - (1-a)  y ==1},{x,y}] /.a-> 10

NSolve[{a  x + y == 0 , 2   x - (1-a)  y ==1},{x,y}] /.a-> 10

Solve[{2 x^2 + y^2 == 1 , 2 x - y ==0},{x,y}]

Eliminate a variable

Eliminate[ {a x + y == 0, 2x + (1-a) y == 1},y]