What is a linear equation? How to solve it? Here, in this
article students will learn about linear equations and ways to solve it. The
linear equation is a simple plain equation that contains simple variables with
no square roots or fraction. It contains variables like x rather than
complicated variables like x2 solving them is simple and you can
solve it in the same way you would solve the simple addition and
subtraction. In these equations instead
of direct value, a variable is given. You have to find its value and then you
will get the result.
However, a linear equation can vary from simple to more
complicated expressions that take time to solve. More advanced methods are thus
used for solving equations. To solve
more complicated problems, students can use equation solver as well. Learn how
to solve the simpler problems before we begin solving more complex problems.
Let’s
learn through examples:
Example
1-
solve equation x-9=3
Solution:
Here, the variable is x whose value we have to find. To solve
for x, we need to eliminate 9 from x to find its value. To undo it, let’s add 9
to one side. Since the equation should be balanced on both sides, so add 9 to
another side as well to make the balance. The equation will look something like
this:
(X-9)+9=3+9
X-9+9= 12
Plus 9 and minus 9 will cancel each other, and thus we
will get the value of x. So, x=12. This is called as addition-subtraction
property.
Note-
always remember that whatever we add or subtract at one side the same goes on
another side to balance the linear equations. If you don’t add/subtract the
same number to both the sides, then you will not get an answer.
You can also check whether the answer is correct or not.
To check put the value of x in the equation.
X=12, on putting the value the equation will become
L.H.S: 12-9=3,
R.H.S: 3, thus L.H.S=R.H.S
Value at both the sides is same; it means the answer is
correct. If you get different values that means your answer is incorrect.
Some linear equations contain variables on both the
sides. Let us learn how to solve such equations by taking next examples.
Example
2-
2x-4=x-6
Solution:
There are two ways to solve the above equation.
The
first method - First, keep the numbers with x on one side
and numbers without variable on another side by changing their signs. The
equation will look like this:
2x-x=-6+4
Solving it will give this answer X=-2. To check it put
the value of x in the original equation.
2(-2)-4= (-2)-6
-8=-8
Thus, a value on L.H.S and R.H.S are same. Hence the
solution is correct.
The
second method- you can solve the above problem using
another method as well. Add 4 to both the sides to make the equation balance.
2x-4+4=x-6+4
2x=x-2
2x-x=-2
x=-2
The value of x is same as that we got from the first
method. You can use the substitution method to check the correctness of the
solution.
To solve more complex problems, you can take help of the equation solver as well.
