Solving of System of Two Equation with Two Variables. Substitution Method

Substitution method consists of following steps:

  1. Transform one of the equations into the form where variable y is expressed in terms of x (or x in terms of y).
  2. In another equation replace y (or x) with obtained expression. As result you will obtain equation with one variable
  3. Find roots of this equation.
  4. Using expression for y in terms of x (or x in terms of y) find corresponding values of y (or x).

Example. Solve system of equations `{(x-3y=10),(x^2-24y=100):}`.

From first equation `x=3y+10`.

Replace x in second equation with this expression: `(3y+10)^2-24y=100` or `y^2-4y=0`. This can be rewritten as `y(y-4)=0`. So, this equation has two roots: y=0 and y=4.

Now, use expression `x=3y+10`.

If y=0 then `x=3*0+10=10`.

If y=4 then `x=3*4+10=24`.

Therefore (10;0) and (24;4) are solutions of the system.