Answer

Verified

407.4k+ views

**Hint:**Here two equations are given which we have to solve by using elimination method. ‘

In this method we have to make one of the coefficients or variables equal for both of the equations.

After making it equal, that coefficient or variable gets cancelled while performing adding or subtracting.

**Complete step by step solution:**

The given equation we have to solve by using elimination method.

The equation given are:

$ 3x+y=5...(i) $

$ x-2y=4...(ii) $

Now, we have to make the $ y $ coefficient equal for both the equations.

For that we have to multiply the equation $ (i) $ by $ 2 $ then we will get,

So,

$ 2\times \left( 3x+y=5 \right) $

$ 6x+2y=10...(iii) $

Now, the equation $ (ii) $ and equation $ (iii) $ have equal $ y $ coefficient with opposite sign, So then it can be cancelled while adding.

So, add equation $ (ii) $ and equation $ (iii) $

$ \left( x-2y=4 \right)+\left( 6x+2y=10 \right) $

$ =7x=14 $

$\Rightarrow x=\dfrac{14}{7} $

$\Rightarrow x=2 $

Put, the $ x=2 $ in equation $ (i) $

$ 3x+y=5 $ (given)

$\Rightarrow 3\times 2+y=5 $

$ \Rightarrow6+y=5 $

Transpose the $ 6 $ to other side of equation

$ y=5-6 $

$\Rightarrow y=-1 $

**Therefore the solution of given equation by elimination method is $ x=2 $ and $ y=-1 $**

**Additional Information:**

There are so many methods of solving the system of equations.

But two of them are most preferable, one is elimination and second is substitution. The elimination method is that, in which we have to add or subtract the given equation for getting an answer of the equation in one variable. In the substitution method, from one equation, the other value of one variable is substituted in another equation.

**Note:**In equation $ (iii) $ we multiply it by $ 2 $ for making the equal $ y- $ coefficient. We can either make the equal $ x $ coefficient of equation $ (i) $ and equation $ (ii) $ . It is done because both the equations have different $ x $ and $ y $ coefficients but for simplifying and further calculation we have to make one of the coefficients equal. Either $ x $ or $ y $ for both the equations.

The calculated solutions can be verified to check whether it satisfies the equation or not which is as follows.

Put $ x=2 $ and $ y=-1 $ in equation $ (i) $

$ 3x+y=5 $

$\Rightarrow 3\times 2+\left( -1 \right)=5 $

$\Rightarrow 6-1=5 $

$ 5=5 $

Now, put $ x=2 $ and $ y=-1 $ in equation $ (ii) $

$ x-2y=4 $

$\Rightarrow 2-2\left( -1 \right)=4 $

$ \Rightarrow2+2=4 $

$ 4=4 $

Hence from the above calculation, the solutions are satisfied by both the equations, therefore the solutions calculated are correct.

Recently Updated Pages

How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE

Mark and label the given geoinformation on the outline class 11 social science CBSE

When people say No pun intended what does that mea class 8 english CBSE

Name the states which share their boundary with Indias class 9 social science CBSE

Give an account of the Northern Plains of India class 9 social science CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

Trending doubts

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Which are the Top 10 Largest Countries of the World?

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

The polyarch xylem is found in case of a Monocot leaf class 11 biology CBSE

Difference Between Plant Cell and Animal Cell

Change the following sentences into negative and interrogative class 10 english CBSE

Casparian strips are present in of the root A Epiblema class 12 biology CBSE