QQuestionAnatomy and Physiology
QuestionAnatomy and Physiology
# PAIR OF LINEAR EQUATIONS IN TWO VARIABLES
## WISE UP
Simultaneous Linear Equations in Two variables : A pair of linear equations in two variables is to form a system of simultaneous linear equations.
Examples: i) $2 x- 3 y= 1$
ii) $x+y= 5$
x+\frac{1}{2} y= 3 \quad x-y= 1
Note : The general form of a pair of linear equations in two variables $x$ and $y$ is
\begin{aligned}
& a_{1} x+b_{1} y+c_{1}= 0 \text { and } \\
& a_{2} x+b_{2} y+c_{2}= 0, \text { where } a_{1}, b_{1}, c_{1}, a_{2}, b_{2}, c_{2} \text { are real numbers and } a_{1}^{2}+b_{1}^{2} \neq 0 \text { and } a_{2}^{2}+b_{2}^{2} \neq 1
\end{aligned}
Solution : A pair of values of the variables $x$ and $y$ satisfying each one of the equations in a give system of two simultaneous linear equations in $x$ and $y$ is called a solution.
Example: For the pair of linear equations
\begin{aligned}
& 3 x- 2 y= 4 \text { and } 2 x+y= 5 \\
& x= 2, y= 1 \text { is a solution. }
\end{aligned}
## GRAPH OF SIMULTANEOUS LINEAR EQUATIONS
We have studied in our previous class that the graph of a linear equation is a straight line. So, th graph of a system of simultaneous linear equations is a pair of straight lines.
Thus, the graph of a system of simultaneous linear equations represents
either a pair of intersecting lines
or a pair of parallel lines
or a pair of coincident lines
## Graphical method :
Consistent system : A system of simultaneous linear equations is said to be consistent if it has atlea one solution.
Note : i) If the system has only one solution then it is called independent.
ii) If the system has infinitely many solutions then it is called dependent.
- Inconsistent system : A system of simultaneous linear equations is said to be inconsistent if it has solution.
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Answer
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Step 1: Identify the given pair of linear equations.
x - y = 1
The given pair of linear equations are:
Step 2: Solve one equation for one variable in terms of the other variable.
x = y + 1
Final Answer
The solution to the given pair of linear equations is $\boxed{\left(\frac{7}{3}, \frac{4}{3}\right)}$.
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