The Substitution Method Solver

Introduction to the substitution method solver:-

In algebra, a linear system of two equations can be solved by two methods. (1) Elimination method (2) substitution method.
If one equation is of the form ax + by +c = 0 and the other equation is of the form px + qy + d = 0 then we can use the substitution
methods by substituting x for y or y for x and solve the equations.
Step 1 : Take the equation ax + by = -c
ax   =  -by - c
x =  -by  - c
a     a
Step 2 : Substitute the value of x in the second equation px + qy +d=0 and find y.
Step 3 : Substitute the value of y in any one of the two given equation and solve for x
Alternatively you can substitute  the value of y in the step 1 equation also to find x
This is called  substitution method solver.

Solve Example by Substitution Methods:-

Here is a problem of linear equation which we are going to solve by substitution methods.
# Solve 2x + 3y = 8 and 5x + 2y = 9
Solution:-
Step 1 : Let us write the first equation 2x + 3y = 8
2x         = 8 - 3y
x          = ( 8 - 3y)/2
Step 2 : Let us substitute the x value in the equation  5x + 2y = 9
5( 8 - 3y)/2 + 2y = 9
( 40 - 15y)/2 + 2y = 9
20 - 7.5 y + 2y   = 9
20 - 5.5y           = 9
Step 3 : Let us subtract 20 from both sides    - 20                    - 20
______________________
- 5.5 y          = - 11
Step 4 : Let us divide both sides by  5.5 we get          -y          = -2
Step 5 : Cancelling negative sign on both sides  we get y = 2
Step 6 : Substituting the value of y = 2  for x = (8 - 3y) /2 we get  (8 - 3*2) / 2
= ( 8 - 6)/2
=  2/2
= 1
Answer  :  x = 1 and y = 2
Step 7 : Let us check our solution by substituting x = 1 and y = 2 in any one of the equation given in the problem
Let us check on 2x + 3y = 8
2(1) + 3(2) gives 2 + 6 = 8 which is the RHS
Hence our solution is correct.

Solving Problem on a Linear Equation by Substitution Method:-

Let us do another linear equation  problem by substitution method:
# Solve 3x + 2y = 7/4 and 2x + 3y  = 2
Solution:
Step 1 : Let us use the first equation to find the value of y
3x + 2y = 7/4
2y = 7/4 - 3x
y = 7/8 - 3x/2
Step 2 : Let us substitute the y value in the equation 2x + 3y = 2
2x + 3( 7  - 3x)  = 2
8      2
2x +  21  - 9x    = 2
8       2
2x - 4.5x       = 2  - 21
8
- 2.5x   = 16 - 21
8
- 2.5x  =  -5/8
- 2.5x  = - 0.625
Step 3 : Let us divide both sides by 2.5 we get        -x   =  - 0.25
x   = 0.25
x   = ¼
Step 4 : Let us substitute x = 1/4 in equation       y = 7  - 3x
8    2
y = 7 - 3*¼
8   2
y = 7 - 3
8   8
y = 4/8
y = ½
Answer : The solution for this problem is x = ¼  and y = ½
Let us check our solution to see if it is correct
Step 1 : substituting x = ¼ and y = ½ in one of the equations say 2x + 3y we get 2*¼ + 3 *½ = 1  + 3 =  2 RHS
2      2
Hence our solution is correct.