# 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.