MATH214
posted by Rebecca .
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

(a) 3y = x  10
substitute in the 2nd equation
3(x2) = 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.