three-variable solution using elimintation: I'm stuck!
I am helping my daughter and this one has me stumped - it is a three-variable equation and their asking her to use "elimination" to solve the problem. The text also states that "If you obtain a false equation, such as 0=1, in any of the steps, then the system has no solution. If you do not obtain a false equation, but obtain an identity such as 0=0, then the system has infinitely many solutions."
#13 in Mcougal Little Algebra 2, pp 182:
Eq#1: 5x + y - z = 6
Eq#2: x + y + z = 2
Eq#3: 3x + y = 4
"bounce" EQ#1 of EQ#2 and eliminate the "z" variable:
5x + y - z = 6
x + y + z = 2
6x + 2y = 8 (New EQ#1')
Bounce EQ#1' against EQ#3 and eliminate the x variable:
6x + 2y = 8 (EQ#1')
-2*(3x + y = 4)
6x + 2 y = 8
-6x - 2y = -8
0 + 0 = 0 (or 0=0, infinitely many solutions).
Did it several times, comes out the same.
Yet the answer in the back of the book gives (0, 4, -2) as the ordered triplet - I plug this into all three equations, and it works!
What gives? and where am I going wrong?
- Jeff (frustrated dad...)