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The objective when dealing with such a pair of equations is to find the values of x and y that satisfy both equations simultaneously Let's imagine a situation, ankita went to a fair in her village. This often involves techniques like substitution, elimination, or graphical methods.

A pair of linear equations in two variables, which has a solution, is called a consistent pair of linear equations Here’s a summary of the most common methods A pair of linear equations which are equivalent has infinitely many distinct common solutions.

Given, the pair of linear equations are

X + 2y = 1 We have to determine the values of a and b for which the pair of linear equations has infinitely many solutions We know that, for a pair of linear equations in two variables be a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0, Is there an error in this question or solution

A pair of linear equations a1x + b1y + c1 = 0 A2x + b2y + c2 = 0 is said to be inconsistent, if ______. In the given figure, graphs of two linear equations are shown The pair of these linear equations is

(a) consistent with unique solutions

(b) consistent with infinitely many solutions (d) inconsistent but can be made consistent by extending these lines When two linear equations in the same variables are taken together they form a pair of linear equations and must be solved together to find the one solution that fits them both These linear equations are grouped together to form a system of simultaneous linear equations

Examples of a system of simultaneous linear equations is shown below. Form the pair of linear equations in the following problems, and find their solutions graphically 5 pencils and 7 pens together cost ₹ 50, whereas 7 pencils and 5 pens together cost ₹ 46 Find the cost of one pencil and that of one pen

Let cost of one pencil be ₹ x and cost of one pen be ₹ y

We are aware that for two linear equations, a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0, respectively If a₁/a₂ = b₁/b₂ c₁/c₂, the chart would comprise of two straight lines, the pair of linear equations is erratic, and there is no solution to the problem For any linear equation, each solution (x, y) corresponds to a point on the line General form is given by ax + by + c = 0

The graph of a linear equation is a straight line Two linear equations in the same two variables are called a pair of linear equations in two variables. When solving a pair of linear equations in two variables, there are several algebraic methods you can use

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