What is a linear equation?
The pair of the linear equation is in the following form-
The most commonly used algebraic methods of solving a pair of linear equations in two variables are –
a) Substitution method
c) Cross Multiplication method
Let’s discuss these methods one by one:
Substitution Method
Here are the steps which we follow while solving a pair linear equations:
Step I – Obtain the two equations. Let the equations be
........................(ii)
Step II – Choose either of the two equations, say (i), and find the value of one variable, say y, in terms of the other, i.e. x.
Step III – Substitute the value of y, obtained in step II, in other equation i.e. (ii) to get an equation in x.
Step IV – Solve the equation obtained in step III to get the value of x.
Step V – Substitute the value of x obtained in step IV in the expression for y in terms of x obtained in step II to get the value of y.
Step VI – The values of x and y obtained in steps IV and V respectively constitute the solution of the given system of two linear equations.
Example: Solve the following system of equations by using the method of substitution:
3x – 5y = -1
x – y = -1
Let, 3x – 5y = -1 … (i)
and x – y = -1 … (ii)
From (ii), we get y = x + 1
Substituting y = x + 1 in (i), we get
3x – 5(x + 1) = -1
-2x – 5 = -1
-2x = 4
x = -2
Putting x = -2 in y = x + 1 we get y = -1
Hence, the solution of the given system of equations is x = -2 and y = -1.
Try these questions now:
1. Solve the following system of equations by using the method of substitution:
x + 2y = -1
2x – 3y = 12
(Answer: x = 3 and y = -2)
2. Solve the following system of equations by using the method of substitution:
2x + 3y = 9
3x + 4y = 5
(Answer: x = -21 and y = 17)
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