# Solve the following system of equation by substitution method $x + y = 7$ and $3x - 2y = 11$

Answer

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**Hint:**In these types of questions we need to eliminate a variable in the form of others and then substitute this in the next equation by solving these two equations we get the values for both variables.

Finally we get the required answer.

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

It is given that the system of equation is $x + y = 7$ and $3x - 2y = 11$

Here we have to find out to solve the system of equations by substitution method.

Let the system of equation are $x + y = 7....(1)$ and $3x - 2y = 11.....(2)$

Now we need to solve these equations by substitution method

From the equation (1)

We can write it as, $y = 7 - x..............(3)$

On substituting the equation $(3)$ in the equation $(2)$

We get the equation,

$ \Rightarrow 3x - 2(7 - x) = 11$

We need to open the brackets by multiplying the terms

$ \Rightarrow $$3x - 14 + 2x = 11$

We added same terms of $x$ variable

$ \Rightarrow 5x - 14 = 11$

Now we took integer to the right handed side

$ \Rightarrow $$5x = 11 + 14$

We just added the right handed side terms

$ \Rightarrow $$5x = 25$

On dividing \[5\] on both sides we get,

\[ \Rightarrow x = \dfrac{{25}}{5}\]

\[ \Rightarrow x = 5\]

Now putting the value of $x = 5$ in equation $(1)$ we get the equation as below:

$ \Rightarrow $$5 + y = 7$

On eliminating the variable $y$, we have

$ \Rightarrow y = 7 - 5$

On subtracting the terms we get,

$ \Rightarrow y = 2$

**Hence we get the values for $x = 5,y = 2$**

**Note:**In this question we have to verify the answer whether it is correct or not

Verifying the answer:

It is given that the equation as $x + y = 7....\left( 1 \right)$

Put the value of $x,y$ in the equation $1$

$5 + 2 = 7$

On adding the terms we get,

$7 = 7$

$\therefore $ The given equation is satisfied.

Hence both the value of $x,y$ are correct.

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