Answer

Verified

372.9k+ views

**Hint:**Use the method of elimination to solve this problem. To solve these types of equations, the first step you need to do is to eliminate one of the variables out. To do this, you must multiply each equation with a constant such that the resultant equation when added or subtracted gives only one equation in its equation. Here, we will multiply the first equation by 1 and the second one by 2. After that we will add those two new equations which will eliminate the variable x and give a value for y. Now put that value of y in equation 1 to get the required value of x.

**Complete step-by-step solution:**

The two fractions we have are

$2x + 3y = 6..........(1)$

And

$x + 2y = 5..........(2)$

Now, we know that to solve these types of problems, we need to eliminate one of the variables first.But how to do it?

You will need to multiply the first equation by and constant ‘a’ and the second equation ‘b’ such that any one of the unknown variables' coefficients becomes 0.

So, following the above steps, lets multiple equation (1) by 1 and equation (2) by 2

After doing this step, we get the modified equations as:-

$2x + 3y = 6..........(3)$

$2x + 4y = 10..........(4)$

Now, subtract equation (4) from equation (3)

We get,

$

(2x + 4y) - (2x + 3y) = 10 - 6 \\

\Rightarrow 2x + 4y - 2x - 3y = 4 \\

\Rightarrow y = 4 \\

$

Therefore, completing this step gave us the value of y as 4

Now putting the value of y in equation (1) we will get

$

2x + 3 \times 4 = 6 \\

\Rightarrow 2x + 12 = 6 \\

\Rightarrow 2x = - 6 \\

\Rightarrow x = \dfrac{{ - 6}}{2} \\

\Rightarrow x = - 3 \\

$

Hence, we got the value of x as -3.

So, the solution of the equations $2x + 3y = 6$ and $x + 2y = 5$is $x = - 3$ and $y = 4$

**Note:**The aim should always be to eliminate only one of the two variables. So, always multiply with such a constant so that you can easily eliminate one of the variables. Also, it is not necessary that you must add the two modified equations. You can also subtract them to get the answer. Use your operator, but make sure you eliminate one variable.

Recently Updated Pages

What are the Advantages and Disadvantages of Algorithm

How do you write 0125 in scientific notation class 0 maths CBSE

The marks obtained by 50 students of class 10 out of class 11 maths CBSE

You are awaiting your class 10th results Meanwhile class 7 english CBSE

Which one of the following was not the cause of the class 10 social science CBSE

Which one of the following cities is not located on class 10 social science CBSE

Trending doubts

Difference Between Plant Cell and Animal Cell

Mention the different categories of ministers in the class 10 social science CBSE

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

Give 10 examples for herbs , shrubs , climbers , creepers

Who is the executive head of the Municipal Corporation class 6 social science CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Which monarch called himself as the second Alexander class 10 social science CBSE

Select the word that is correctly spelled a Twelveth class 10 english CBSE

Write an application to the principal requesting five class 10 english CBSE