Substitution Method Steps
- Simplify the given equation by expanding the parenthesis
- Solve one of the equations for either x or y
- Substitute the step 2 solution in the other equation
- Now solve the new equation obtained using elementary arithmetic operations
- Finally, solve the equation to find the value of the second variable
What is substitution method?
The substitution method is one of the categories of the algebraic method to solve the pair of linear equations. From the word substitution, we understand that the method majorly includes substituting certain values. In this method, we write the value of one variable in terms of another variable. Then we have to substitute the value of the variable in another equation. In this way, the equation becomes a linear equation in one variable that can easily be solved.
What is the graphical method?
Another name for the graphical method is the geometric method used to solve the system of linear equations. In this method, the equations are designed based on the objective function and constraints. Different steps are involved in obtaining the solution of simultaneous equations by graphical method.
How to verify whether a solution obtained is correct or not?
To verify whether the solution obtained is correct or not, substitute the values of x and y in any of the given systems of equations.
When do you get a unique solution?
You will get a unique solution only when you get a proper value of the unknown variable after substitution.
What are Simultaneous Equations?
The simultaneous equation is an equation which involves two or more quantities that are related using two or more equations. It includes a set of few independent equations. The simultaneous equations are also known as the system of equations, in which it consists of a finite set of equations for which the common solution is sought. To solve the equations, we need to find the values of the variables included in these equations.
How to find the coefficient of a variable?
Step 1: The coefficient of variable ’b’ is equal and has the opposite sign to the other equation. Add the equations 1 and 2 to eliminate the variable ‘b’. Step 2: The like terms will be added. Step 3: Bring the coefficient of a to the R.H.S of the equation.
What is an equation in math?
In Mathematics, an equation is a mathematical statement in which two things should be equal to each other. An equation consists of two expressions on each side of an equal sign (=). It consists of two or more variables.
Is L.H.S equal to R.H.S?
In short, the L.H.S value should be equal to R.H.S value. While substituting the values of the variables in an equation, it should prove its equality. There are different types of equations in Maths, such as: Linear Equation. Quadratic Equation.
Differentiated Learning Objectives
All students should be able to solve a pair of equations simultaneously using the method of substitution.
Solving Simultaneous Equations by Substitution
Solving simultaneous equations by substitution is an alternative approach to the elimination method. The best method to use depends on the coefficients in the equations. We use the substitution method when x or y appears with a coefficient of one in either of the two equations.
Plenary
The plenary challenges students to form their pair of equations by equating the two equal sides of a rectangle. When I present this question to the class, I give them about 3 minutes to develop an approach. If students struggle to get started, I demonstrate how to form an equation by equating the two equal widths.
Differentiation
More able students could quickly progress to the later questions in the included worksheet, setting up equations from real-life problems. Less able students could focus on solving equations in which one equation is given x or y.
Additional Resources
How to solve a pair of simultaneous equations using the substitution method.
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Graphical Method
Algebraic Method
- This method mainly involves algebraic operations to solve the pair of equations with two variables. The algebraic method is classified into three categories: 1. Substitution method 2. Elimination method 3. Cross-multiplication method This article will discuss one of the algebraic methods called the “Substitution Method” in detail.
Definition of Substitution Method
- The substitution method is one of the categories of the algebraic method to solve the pair of linear equations. From the word substitution, we understand that the method majorly includes substituting certain values. In this method, we write the value of one variable in terms of another variable. Then we have to substitute the value of the variable in another equation. In this way, th…
Steps Involved in Substitution Method
- Suppose we are given a pair of linear equations in two variables, say \(x\) and \(y.\) To solve these equations by the method of substitution, we follow the below-given steps: Step 1:Consider any one equation out of the two and express \(y\) in terms of \(x\) or vice versa. Step 2:Substitute this value of \(y\) in terms of \(x\) in another equation...
Example
- Let us assume the system of linear equations: \(4x+5y=23\) and \(x-2y=-4\) Given: \(4x+5y=23 … (1)\) \(x-2y=-4…(2)\) The equation \((2)\) can be written as, \(⇒x=2y-4…….(3)\) Now, in equation \((1)\) eliminate \(x\) by substituting the equation \((3).\) Hence, equation \((1)\) becomes, \(4(2y-4)+5y=23\) Applying the distributive property for the above equation, \(8y-16+5y=23\) Now, solv…
Solved Examples
- Q.1. Solve \(5x+y=11\) and \(3x+2y=15\) Ans: Given, \(5x+y=11\) and \(3x+2y=15\) For solving simultaneous equations, Let, \(5x+y=11……..(1)\) and \(3x+2y=15……..(2)\) From Equation \((2)\) we get, \(y = \left( {\frac{{15 – 3x}}{2}} \right) \ldots \ldots \ldots ..(3)\) In the substitution method, we find the value of one variable in terms of other variables and then substitute it back. Substitu…
Summary
- In this article, we learned that there are two methods of solving simultaneous linear equations. Then, we studied one of the algebraic methods of solving the pair of equations: the substitution method. We understood the meaning of the substitution method and then learnt the steps involved in solving pair of linear equations by the substitution method. Lastly, we have solved ex…
Frequently Asked Questions
- Q.1. What is systems of equations by substitution? Ans:In mathematics, the system of equations by substitution are pair of linear equations that have to be solved simultaneously using the substitution method. Here, we solve the equation by converting it into the equation in one variable by substitution. Then, back substitute the value of the variable in another equation. Q.2. What ar…