Use back substitution to solve the following systems Enter y

Use back substitution to solve the following systems. Enter your answers as points. (E.g., if the solution is x_1 = 2, x_2 = -1 you would enter (2,-1) Do not forget the parentheses and commas.) (a) 2x_1 - x_2 = -7 3x_2 = 9 (x_1, x_2) = (b) x_1 + 2x_2 - x_3 = -8 3x_2 + 3x_3 = -15 x_3 = 0 (x_1, x_2, x_3) = (c) 4x_1 - 2x_2 + x_3 = 0.5 x_2 - 3x_4 = 4 - 2x_3 + 3x_4 = -8 x_4 = -1 (x_1, x_2, x_3, x_4) =

Solution

.a. 2x₁-x₂=-7

3x₂=9

x₂=3

Substituting back the value of x₂ in first equation we get

2x₁-3=-7

x₁=-2

Solution is (-2,3)

b.x₁+2x₂-x₃=-8

3x₂+3x₃=-15

x₃=0

Plugging back the value of x₃ we get

3x₂=-15

x₂=-5

Substituting back the values of x₂ and x₃ we get

x₁-10=-8

x₁=2

Solution is (2,-5,0)