Question

Consider the sum of angle in a triangle the second angle is 50 degree less than four times the first angle, the third angle is 40 degree less than the first angle
a) from the above statements extract the system of linear equation
b) used guassian elimination to solve the equation you extracted.

Answer 1

х - I

у - II

z - III

х + у + z = 180

x-z = 40

4x-у = 50

$\begin{pmatrix} 1 & 1&1&180 \\ 1 & 0&-1&40\\ 4&-1&0&50 \end{pmatrix}$ multiply the second line by -4 and add it to the third line $\begin{pmatrix} 1 & 1&1&180 \\ 1 & 0&-1&40\\ 0&-1&4&-110 \end{pmatrix}$ multiply the second line by -1 and add the first line $\begin{pmatrix} 1 & 1&1&180 \\ 0 &1&2&140\\ 0&-1&4&-110 \end{pmatrix}$ add the second line to the third line $\begin{pmatrix} 1 & 1&1&180 \\ 0 &1&2&140\\ 0&0&6&30 \end{pmatrix}$

6z = 30

z = 5

у + 10 = 140

у = 130

х + 5 + 130 = 180

х = 45

Answer: 45 ⁰ , 130 ⁰ , 5 ⁰.