CBSE 10
CBSE 10 Algebra: Solve Linear Equations in Two Variables Like a Pro
May 7, 2024
Aha
Language
English
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A pair of linear equations in two variables is a set of two linear equations in two variables that are to be solved together. We can represent this pair of linear equations in two variables in two ways: graphical representation and algebraic methods.
The pair of linear equations in two variables can be represented using the following form:
ax + by = c
dx + ey = f
where a, b, c, d, e, and f are constants, and x and y are variables.
Graphical representation is an effective method to solve pair of linear equations in two variables. We can plot both equations on the same graph and find the intersection point of these two lines. The intersection point is the solution to the pair of linear equations in two variables.
There are three algebraic methods of solving a pair of linear equations in two variables:
In this method, we solve one equation for one variable and then substitute it into the other equation to find the value of the other variable.
In this method, we add or subtract the two equations to eliminate one of the variables and then solve for the other variable.
In this method, we multiply one equation by a constant and then add or subtract the two equations to eliminate one of the variables and then solve for the other variable.
Solve the following pair of linear equations in two variables using the substitution method:
2x + 3y = 5
5x - y = 7.
✅ Solution:
1. From the second equation, we can write y = 5x - 7.
2. Substituting this value of y into the first equation, we get 2x + 3(5x - 7) = 5.
3. Simplifying the equation, we get 17x = 26.
4. Therefore, x = 26/17.
5. Substituting this value of x into the second equation, we get 5(26/17) - y = 7.
6. Simplifying the equation, we get y = 11/17.
7. Therefore, the solution to the pair of linear equations in two variables is (x,y) =
(26/17,11/17).
Solve the following pair of linear equations in two variables using the elimination method:
3x + 2y = 1
5x - 4y = 14.
✅ Solution:
1. Multiplying the first equation by 2 and the second equation by 1, we get
6x + 4y = 2
5x - 4y = 14.
2. Adding the two equations, we get 11x = 16.
3. Therefore, x = 16/11.
4. Substituting this value of x into the first equation, we get 3(16/11) + 2y = 1.
5. Simplifying the equation, we get y = -37/22.
6. Therefore, the solution to the pair of linear equations in two variables is (x,y) =
(16/11,-37/11).
A pair of linear equations is consistent if it has one unique solution.
A pair of linear equations is inconsistent if it does not have any solution.
If an equation has the highest degree of 1, then it is called a linear equation.
If an equation has the highest degree of 2, then it is called a quadratic equation.
If an equation has the highest degree of 3, then it is called a cubic equation.
In conclusion, the pair of linear equations in two variables is an important concept in mathematics that has various applications in real life. It is crucial to understand the different methods of solving these equations and their graphical representation to solve real-life problems. If you want to learn more about mathematics, check out Aha AI to access a wide range of resources and practice problems.
