Question

Solve the system of equations.
x plus 3 y
equals0
9y
equalsminus3x
Question content area bottom
Part 1
Solve the first equation for x.
x plus 3 y
equals0
x
equals
  
negative 3y
Part 2
Substitute.
9yequalsnegative 3 left parenthesis nothing right parenthesis

Answer 1

Part 1
x + 3y = 0 ⇒ x = −3y.

Part 2
Substitute x = −3y into 9y = −3x:
9y = −3(−3y) = 9y.

This is an identity, so every y works. The system has infinitely many solutions: all pairs with x = −3y (e.g. (x,y) = (−3t, t) for any real t).