System of equations

• How much ways there are to solve a system of equations?

  There are 5 ways:

  Scholar way, Subtraction method, Kramer's metod, Inverse matrix method, Gauss's metod
• How to solve a system of equation with scholar method?

  1. Describe one variable with anothers
  2. Put described variable into other equations
  3. Continue until solved
• How to use subtraction method?

  1. Substract (or add) one equation in the system to another (if there are same coefficients at the same variable)
  2. Find other variable
  3. Put found variable into other equations
  4. Continue until solved
• First step of Kramer's method?

  Find the determinant of a matrix $\begin{bmatrix}a_1 & b_1 \\ a_2 & b_2\end{bmatrix}$

  If not equal to 0, then continue, if equal, then system doesn't have answer or have an infinity as an answer.
• Second step of Krame's method?

  Find the determinants:

  $det|x| =$$\begin{bmatrix}c_1 & b_1 \\ c_2 & b_2\end{bmatrix},det|y| =$$\begin{bmatrix}a_1 & c_1 \\ a_2 & c_2\end{bmatrix}$
• Third step of Kramer's method?

  Divide det x by determinant from the first step to get x, divide det y by determinant from the first step to get y.
• How much steps there are in inverse matrix method?

  There are 5 steps In this method
• What steps are in matrix method?

  1. Make 3 matrices - 1 with coefficients at the variables, 1 with variables and 1 with results of operations with variables
  2. Find determinant of matrix with coefficients
  3. If determinant equals 0, then there is no solution or infinite amount of solutions, else continue
  4. Find matrix of co-factors (Minors with special signs)
  5. Multiplicate 1 divided by determinant of matrix of coefficients, matrix of cofactors and matrix with results