PUMPA - SMART LEARNING
எங்கள் ஆசிரியர்களுடன் 1-ஆன்-1 ஆலோசனை நேரத்தைப் பெறுங்கள். டாப்பர் ஆவதற்கு நாங்கள் பயிற்சி அளிப்போம்
Book Free DemoA linear equation in which two variables are involved in which each variable is in the first degree.
It can be written in the form of \(ax + by + c = 0\) where \(a\), \(b\), and \(c\) are real numbers, both \(a\) and \(b\) are not equal to zero, \(x\) and \(y\) are variables and \(c\) is a constant.
It can be written in the form of \(ax + by + c = 0\) where \(a\), \(b\), and \(c\) are real numbers, both \(a\) and \(b\) are not equal to zero, \(x\) and \(y\) are variables and \(c\) is a constant.
Example:
\(2x + y = 8\), \(x - y - 1 = 0\), \(y = 2x\) are examples of linear equations in two variables.
We have also learnt about the solution of an equation.
A solution of an equation is a number substituted for an unknown variable which makes the equality in the equation true.
Example:
Consider the equation \(x + 3 = 2y - 1\). Check whether \(x = 0\) and \(y = 2\) is the solution of the equation.
Solution:
Simplifying, we have:
\(x - 2y = -4\)
To verify whether \(x = 0\) and \(y = 2\) is the solution of the equation, let us substitute \(x = 0\) and \(y = 2\) in the given equation.
LHS \(= 0 - 2(2) = 0 - 4 = -4 =\) RHS
Therefore, \(x = 0\) and \(y = 2\) is the solution of the equation.
Geometrically, we can plot this point \((0,2)\) on the line \(x + 3 = 2y - 1\). This implies that every solution of the equation is a point on the line representing it.
Register for free to see more content