Linear Equations by Substitution Calculator

In algebra, Linear Equations is the most essential concept. Solving linear equations can be tricky, but it can be solved easily using the substitution method. Solving Systems of Linear Equations with Substitution is simplifying the coordinates or coefficients or variable values by substituting one equation of solved expression into another equation. 

How to Solve a System of Equations by Substitution Method? 

The process of solving systems of equations by substitution methods is simple yet quick to find the variables. Here, we have discussed solving the system of equations by substitution in detailed steps to learn the calculation of equations manually. Follow them 

1. In the first step, take one linear equation and solve it for y in terms of x. 
2. After that, substitute the result in another linear equation. 
3. Solve the expression, then you have the x-coordinate or x value. 
4. Substitute the x value in one equation and find the second coefficient or coordinate ie., y value. 
5. Hence, the solutions of systems of linear equations by substitution are obtained easily. 

Example:

Solve the following linear equation in two variables using substitution:

x+2y=2x−5

x−y=3

Solution: 

Given equations are 

x+2y=2x−5 ……(1)

x−y=3 …..(2)

Isolate x+2y=2x−5 for x

x+2y=2x−5 

x=5+2y ….(3)

Substitute (3) in (2)

x-y=3

5+2y-y=3

5+y=3

y=3-5

y = -2

Substitute the y value in equation (1)

x+2y = 2x-5

x-4 = 2x-5

2x-5-x+4 = 0

x-1=0

x=1

Hence, the solutions to the system of equations by substitution is x=1, y=-2.