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Substitution Method Calculator
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Substitution Method Calculator known as substitution calculator is an online tool to find solution of given two equations. If any two system of equations are given then it solves it by substitution method and gives you the variable value hence called as solving systems of equations by substitution calculator. It is a  substitution solver that makes calculation easy and fun. If two equations are given, then it can easily find the solution of those equations is a solving by substitution calculator.
 

Steps for Substitution Method

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Step 1 :  

Select the easiest equation and solve that for variable either x = or y = .



Step 2 :  

Substitute the equation from step1 into other equation and solve for new equation and then solve for second variable.



Step 3 :  

The solution of x and y is written as an order pair.



Examples on Substitution Method Calculator

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  1. Solve the following equations by substitution method. -x + y = 1. 2x + y = -2.?


    Step 1 :  

    Now, 2x + y = -2.


    Substitute y = x + 1 in the above equation.


    So, 2x + x + 1 = -2.


    = 3x + 1 = -2.


    Take -1 on both the sides.


    3x + 1 - 1 = -2 - 1.


    3x = -3.


    Divide by 3 on both the sides


    So x = -1.



    Step 2 :  

    Now y = x + 1.


    Substitute x = -1 in above equation.


    y = -1 + 1.


    Hence y = 0.



    Answer  :  

    So, x = -1 and y = 0
    The solution is (x, y) = (-1, 0).



  2. Solve the following equations by substitution method. 4x + y = 11. x + 2y = 8?


    Step 1 :  

    Let us consider the equation: 4x + y = 11.


    So add  -4x on both the sides. -4x + 4x + y = 11 - 4x.


    So y = 11 - 4x.



    Step 2 :  

    Now, x + 2y = 8.


    Substitute y = 11 - 4x in the above equation.


    So, x + 2(11 - 4x)= 8. x + 22 - 8x = 8. -7x + 22 = 8.


    Take -22 on both the sides.


    So, -7x + 22 - 22 = 8 - 22. -7x = - 14.


    Divide by -7 on both the sides.


     x = 2.



    Answer  :  

    So, x = 2 and y = 3
    The solution is (x, y) = (2, 3).



  3. Two software companies, company A and company B, planned separate trips for their employees. Software company A rented and filled 6 cabs and 2 bikes with 22 employees. And software company B rented and filled 9 cabs and 4 bikes with 35 employees. Each cab and each bike carried the same number of employees. Find the number of employees in each cab and in each bike.


    Step 1 :  

    Software company A, rented 6 cabs + 2 bikes for 22 employees.
    Software company B, rented 9 cabs + 4 bikes for 35 employees.



    Step 2 :  

    Let x be the number of employees in one cab and y be the number of employees in one bike. Then
    According to the statement:
    6x + 2y = 22 .....................(1)
    9x + 4y = 35 …………….. (2)
    Solve for x and y
    Multiply both sides of the equation (1) by 2 and subtract equation (2) from new equation, we get
    12x + 4y = 44
    -9x - 4y = -35
    --------------------
    3x + 0y = 9
    ----------------------
    Or x = 3
    Now, plugin back x = 3 in equation (1)
    6(3) + 2y = 22
    18 + 2y = 22
    2y = 22 -18
    2y = 4
    y = 2



    Answer  :  

    Therefore, each cab and each bike carried 3 and 2 respective number of employees.



  4. An online shopping company offered discount on some accessories. In that, cost of eight hats and four bracelets is 176 dollars and cost of two hats and two bracelets is 48 dollars. What is the cost price of one hat and one bracelet?


    Step 1 :  

    Suppose that cost of 1 hat is x dollars and cost of 1 bracelet is y dollars.



    Step 2 :  

    Construct a system of equation using given information.
    8x + 4y = 176 …………(1)
    2x + 2y = 48  …………..(2)
    (2) => x + y = 24
    Or y = 24 – x  ………(3)
    Substitute the value of y in equation (1), we obtain
    8x + 4 (24 – x) = 176
    8x + 96 – 4x = 176
    4x = 176 – 96
    4x = 80
    Or x = $\frac{80 }{ 4} $ = 20
    Again, plug in the value of x in (3)
    y = 24 – 20 = 4



    Answer  :  

    Cost of 1 hat = 20 dollars.
    And the cost of 1 bracelet = 4 dollars.



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