3. Given the system of linear equations a+b+c=2 2a.3br::3 a+b+20:2 3a2b3620 determine if a solution exists. If it does, what is the solution? A) (lg1,2) C) (2,1,2) E) *No unique solution ex B) (2:1,0) D) (131:1) ists. 4. Given the system of linear equations 2x1 - X2 + 23 = -1 8x1 - 4x2 - 23 = -4 2x1 - 22 = -1 determine if a solution exists. If it does, what is the solution? A) *Let t be a variable such that t goes from negative infinity to positive infinity. The solution set is (t - 7, t, 0). B) Let t be a variable such that t goes from 0 to positive infinity. The solution set is ($t, 3t-?, t) C) Let t be a variable such that t goes from negative to positive infinity. The solution set is (t, 3t - }, t) D) Let t be a variable such that t goes from negative to positive infinity. The solution set is ( 8 t + 5, -;t, t). E) None of the above.Option A: t be a variable such thatt goes from negative infinity to positive infinity. The solution set is (it 5, t, 0). 1. 2 (it i) t l 0 :t t : 0 35 1(Nottruefor Equation 1) 8G1! ) 4t 0 : 4t 4t : U 35 4 (Not true for Equation 2) 2 (t %) t : f t: 0 7E 1 (Not true for Equation 3) Option A does not satisfy the system of equations. Option E: None of the provided options satisfy the system of equations. Therefore, the correct answer is E. None of the above. Now, let's solve the system of linear equations using the augmented matrix method. The given system of equations is: 1. 2:171 1'2 l 13 : 1 2. 8131 4.32 13 : 4 3. 2:21 1'2 : 1 This system can be represented as an augmented matrix 1 0.5 0 0.5 0 0 1 2 0 0 1 0 This system is inconsistent, which means there is no solution that satisfies all three equations. 80, there is no solution that exists for this system of linear equations