Answer
Verified
412.2k+ views
Hint: The above given expression is an example of a two step equation. In order to solve it we need to manipulate the given equation in such a way that we should get $y$ by itself. In order to get $x$ by itself we can perform any arithmetic operations on both LHS and RHS equally at the same time such that the equality of the given equation doesn’t change.
Complete step-by-step solution:
Given
${\left( {y - 3} \right)^2} = 4y - 12..................................\left( i \right)$
Now in order to solve the given equation we need to solve for $y$.
Such that we have to manipulate the given equation in terms of only $y$, which can be achieved by performing different arithmetic operations on both LHS and RHS equally.
So to isolate the $y$ term from equation (i) first we have to take 4 common from both the terms in the RHS.
Such that:
\[
\Rightarrow {\left( {y - 3} \right)^2} = 4y - 12 \\
\Rightarrow {\left( {y - 3} \right)^2} = 4\left( {y - 3} \right).......................................\left( {ii} \right) \\
\]
Now we can see that $\left( {y - 3} \right)$ is common to both RHS and LHS such that one $\left( {y - 3} \right)$ can be cancelled.
So we get:
\[
\Rightarrow {\left( {y - 3} \right)^2} = 4\left( {y - 3} \right) \\
\Rightarrow \left( {y - 3} \right) = 4..........................\left( {iii} \right) \\
\]
Now to isolate the term $y$ we have $ + 3$ to both LHS and RHS, since adding $ + 3$ to the LHS will cancel the term $ - 3$.
Such that:
\[
\Rightarrow \left( {y - 3} \right) = 4 \\
\Rightarrow y - 3 + 3 = 4 + 3 \\
\Rightarrow y = 7..............................\left( {iv} \right) \\
\]
Therefore on solving ${\left( {y - 3} \right)^2} = 4y - 12$ we get\[y = 7\].
Note: A two-step equation is an algebraic equation which can be solved in two steps. The equation is said to be true when we find the value of the variable which makes the equation true. We can also check if the value of the variable that we got is true or not by substituting the value of the variable back into the equation and checking whether it satisfies the given equation or not.
Complete step-by-step solution:
Given
${\left( {y - 3} \right)^2} = 4y - 12..................................\left( i \right)$
Now in order to solve the given equation we need to solve for $y$.
Such that we have to manipulate the given equation in terms of only $y$, which can be achieved by performing different arithmetic operations on both LHS and RHS equally.
So to isolate the $y$ term from equation (i) first we have to take 4 common from both the terms in the RHS.
Such that:
\[
\Rightarrow {\left( {y - 3} \right)^2} = 4y - 12 \\
\Rightarrow {\left( {y - 3} \right)^2} = 4\left( {y - 3} \right).......................................\left( {ii} \right) \\
\]
Now we can see that $\left( {y - 3} \right)$ is common to both RHS and LHS such that one $\left( {y - 3} \right)$ can be cancelled.
So we get:
\[
\Rightarrow {\left( {y - 3} \right)^2} = 4\left( {y - 3} \right) \\
\Rightarrow \left( {y - 3} \right) = 4..........................\left( {iii} \right) \\
\]
Now to isolate the term $y$ we have $ + 3$ to both LHS and RHS, since adding $ + 3$ to the LHS will cancel the term $ - 3$.
Such that:
\[
\Rightarrow \left( {y - 3} \right) = 4 \\
\Rightarrow y - 3 + 3 = 4 + 3 \\
\Rightarrow y = 7..............................\left( {iv} \right) \\
\]
Therefore on solving ${\left( {y - 3} \right)^2} = 4y - 12$ we get\[y = 7\].
Note: A two-step equation is an algebraic equation which can be solved in two steps. The equation is said to be true when we find the value of the variable which makes the equation true. We can also check if the value of the variable that we got is true or not by substituting the value of the variable back into the equation and checking whether it satisfies the given equation or not.
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
Give 10 examples for herbs , shrubs , climbers , creepers
Change the following sentences into negative and interrogative class 10 english CBSE
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
How do you graph the function fx 4x class 9 maths CBSE
Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE
Application to your principal for the character ce class 8 english CBSE
Write a letter to the principal requesting him to grant class 10 english CBSE