There are two necessary conditions in solving system of equations by substitution

1. Number of equations should be equal to number of variables. If there are two variables, there must be two equations; 3 Variables = 3 Equations etc.,

2. One of the equations can easily be solved for one variable.

Given below are the steps to be considered for solving system of equations using substitution method.

1. Select one equation and isolate one variable and name it as first equation.

2. In second equation substitute the value of the first equation and solve for the variable.

3. Again by substituting in the given equations the value of the second variable is found. This process is continued until the values for the given variables are known.

### Solved Example

**Question: **x + y =3

y - 2x = 5

** Solution: **

The given equations are : x + y = 3 .................(1)

y - 2x = 5 ................(2)

Step -1 : From the first equation we isolate x (y can also be isolated).

$\Rightarrow$ x = 3 - y.

Step -2 : Substitute x = 3 - y in the second equation.

$\Rightarrow$ y - 2(3 - y) = 5

Step -3 : Solve for y

y - 6 + 2y = 5

$\Rightarrow$ 3y = 11

$\Rightarrow$ y = $\frac{11}{3}$

Step -4 : As the value of y is known. The value of x can be easily found now by substituting in any of the given equations.

Substituting in x = 3 - y we get y as

x = 3 - $\frac{11}{3}$

3x = 9 - 11

x = $\frac{-2}{3}$

Therefore, x = $\frac{-2}{3}$ and y = $\frac{11}{3}$.

Verification can be done by plugging the values of x and y in one of the given equations.