SOLUTION: Solve each system by substitution. Determine whether each system is independent, inconsistent, or dependent 3x - 2y = 7 -3x + y = 5

Algebra ->  Matrices-and-determiminant -> SOLUTION: Solve each system by substitution. Determine whether each system is independent, inconsistent, or dependent 3x - 2y = 7 -3x + y = 5      Log On


   

Question 44238This question is from textbook College Algebra
: Solve each system by substitution. Determine whether each system is independent, inconsistent, or dependent
3x - 2y = 7
-3x + y = 5 This question is from textbook College Algebra

Answer by fractalier(6550) About Me  (Show Source):
You can put this solution on YOUR website!
From
3x - 2y = 7
-3x + y = 5
we can solve the second one for y and substitute it into the first one, so we get
y = 3x + 5 and then
3x - 2(3x + 5) = 7
3x - 6x - 10 = 7
-3x - 10 = 7
-3x = 17
x = -17/3
If we plug that in to the first equation and get
3(-17/3) - 2y = 7
-17 - 2y = 7
-2y = 24
and finally
y = -12
Our solution is (-17/3, -12) and our system is consistent and independent.