Solve each of the following systems. (a) x1 2x2 = 5 3x1 + x2 = 1 (b) 2x1 + x2 = 8 4x1

QUESTION:

Solve each of the following systems.

(a) \(\begin{aligned} x_{1}-2 x_{2} & =5 \\ 3 x_{1}+x_{2} & =1 \end{aligned}\)

(b) \(\begin{array}{l} 2 x_{1}+x_{2}=8 \\ 4 x_{1}-3 x_{2}=6 \end{array}\)

(c) \(\begin{array}{l} 4 x_{1}+3 x_{2}=4 \\ \frac{2}{3} x_{1}+4 x_{2}=3 \end{array}\)

(d) \(\begin{aligned} x_{1}+2 x_{2}-x_{3} & =1 \\ 2 x_{1}-x_{2}+x_{3} & =3 \\ -x_{1}+2 x_{2}+3 x_{3} & =7 \end{aligned}\)

(e) \(\begin{array}{l} 2 x_{1}+x_{2}+3 x_{3}=1 \\ 4 x_{1}+3 x_{2}+5 x_{3}=1 \\ 6 x_{1}+5 x_{2}+5 x_{3}=-3 \end{array}\)

(f) \(\begin{aligned} 3 x_{1}+2 x_{2}+x_{3}= & 0 \\ -2 x_{1}+x_{2}-x_{3} & =2 \\ 2 x_{1}-x_{2}+2 x_{3} & =-1 \end{aligned}\)

(g) \(\begin{aligned} \frac{1}{3} x_{1}+\frac{2}{3} x_{2}+2 x_{3} & =-1 \\ x_{1}+2 x_{2}+\frac{3}{2} x_{3} & =\frac{3}{2} \\ \frac{1}{2} x_{1}+2 x_{2}+\frac{12}{5} x_{3} & =\frac{1}{10} \end{aligned}\)

(h) \(\begin{aligned} x_{2}+x_{3}+x_{4} & =0 \\ 3 x_{1}+3 x_{3}-4 x_{4} & =7 \\ x_{1}+x_{2}+x_{3}+2 x_{4} & =6 \\ 2 x_{1}+3 x_{2}+x_{3}+3 x_{4} & =6 \end{aligned}\)