Question

CRITICAL THINKING Find the values of a, b, and c so that the linear system shown has (---1. 2. --3) as its only solution. Explain your reasoning. x + 2y - Bra -r-y +z = b 2x + 3y - 2z=c enter your answer as follows: a=_,b=_,c=__without any spaces. Show Your Work

Answer 1

1) Let's set the system of linear equations:

x +2y -3z = a

-x -y +z = b

2x +3y -2z =c

2) Since the solution has already been given ( -1,2,-3) all that's left to do, is to plug it into each equation so that we can find a, b and c. Just like this:

x +2y - 3z = a ⇒ (-1) +2(2) -3(-3) = a ∴ a = 4

-x -y +z = b ⇒ -(-1) -(2) +(-3) = b ∴ b = 0

2x +3y -2z =c ⇒ 2(-1) +3(2) -2 (-3)=c ∴ c = -2

3) Hence, a = 4 b = 0 and c = -2