Question

Solve each of the following systems, if possible. Indicate whether the system has a unique solution, infinitely many solutions or no solution.

(a) 3y = x – 10
y = x – 2

(b)x + y = 5
3x + 3y = 15

Answer 1

(a) 3y = x - 10
substitute in the 2nd equation
3(x-2) = x - 10
3x - 6 = x - 10
simplifing...
2x = -4 or x = -2 and y = -4
this is a unique solution
(b) this system has infinitely many solutions and cannot be solved without more information.

3x + 3y = 15
divide equation by 3
(3/3)x + (3/3)y = 15/3 or
x + y = 5
so the equations are essentially identical.