Solving a system of equations might seem scary, particularly for high school students, because it involves finding the value of two unknown variables in two equations.
However, there is a method called the substitution method that can simplify the process and make it less intimidating.
Read on to find out a step-by-step guide on how to solve systems of equations by substitution method. You might also enjoy reading: PEMDAS vs. BODMAS vs. BIDMAS: How do they differ?
What Is The Substitution Method?
The substitution method is an algebraic method for solving linear equations systems that involve substituting the value of one variable from one equation into the other.
The substitution method involves the followings steps:
- Choose one equation and solve for one of the variables.
- Substitute (plug-in) the expression you found into the other equation and solve.
- And then, resubstitute the value into the initial equation to find the corresponding variable.
How Do You Solve Substitution Method Questions?
The substitution method is a great way to solve systems of equations. Here are detailed step-by-steps on how to solve systems of equations using the substitution method.
Step 1: Choose Any of The Two Equations
The first step in the substitution method is to choose any of the two equations and use it to form an expression. You can choose the equation that is easier to solve for one variable.
For example, if one equation is expressed in terms of x and y and the other in terms of x and z, you will choose the equation that is expressed in terms of x and y.
For instance, two equations can be represented as follows:
- x + y = 4
- x – y = 2
Step 2: Solve For One Variable
To solve the system below using the substitution method, we need to isolate one of the variables in one of the equations and substitute it into the other equation.
In this case, we can isolate x from the second equation by adding y to both sides, which gives us the following:
- x = y + 2
Step 3: Substitute The Found Value in The Other Equation
Next, substitute the expression for x in the first equation and solve for the second variable, which will give you an equation in terms of one (y) variable only.
- (y + 2) + y = 4
Step 4: Solve For The Second Variable
Solve the equation obtained in step 3 to get the value of the second variable.
- 2y = 2
- y = 1
Step 5: Substitute The Value of y Into One of The Original Equations
- x + 1 = 4
- x = 3
Therefore, the solution of the system of equations is x = 3 and y = 1.
Step 6: Check The Values
After obtaining the values of both variables, substitute the values in both equations to check if they satisfy both equations. If the values of the variables satisfy both the equations, then it is the solution of the two equations.
Example Of The Substitution Method
Let us explore a more complex example. Consider the following system:
- 2x + y = 12
- x – y = 4
We again start by isolating one of the variables in one of the equations, say x in the second equation:
- x = y + 4
Substitute this expression for x in the first equation:
- 2(y + 4) + y = 12
Simplify the equation:
- 3y + 8 = 12
- 3y = 4
- y = 4/3
Substitute the value of y in the expression for x:
- x = (4/3) + 4
- x = 16/3
The solution of this system is x = 16/3 and y = 4/3.
Tricks And Tips For Solving Systems of Equations Using The Substitution Method
Let us discuss some tricks and tips for solving systems of equations using the substitution method.
- One such trick is to always check our solution by substituting the values of x and y into both equations.
- If the substitution makes both equations true, then we have the correct solution.
- Another tip is to avoid fractions by multiplying both sides of each equation by a common denominator.
If you want to learn more about how to use the substitution method, I recommend you check out this excellent free course from Khan Academy or watch this video or the video below.
What to read next:
- What a tangent line is, how to calculate it, and its importance.
- Here’s How To Use The Order of Operations (PEMDAS).
- What is the FOIL Method for Binomial Multiplication (Including examples)
Wrapping Up
The substitution method is an effective strategy for solving systems of equations. It involves isolating one of the variables in one of the equations and substituting it into the other equation.
This method works well for simple systems and is easy to understand; however, I encourage you always to check your answers for accuracy.
I believe that with enough practice, you will master the substitution method and be able to solve more complicated systems with ease.