Question

How do you solve $ y = {x^2} $ , $ y = 2x $ using substitution?

Answer 1

Hint: Here we are given the set of equations in which the left hand side of the equations are equal and so we can substitute the values of it in one another equations resulting into one new equations with one variable and then will simplify for the resultant required value.

Complete step by step solution:
Take the given expression:
 $ y = {x^2} $ ….. (A)
 $ y = 2x $ ….. (B)
Take the equation (A)
 $ y = {x^2} $
Now, substitute the values of “y” in the above equation from the equation (B)
 $ 2x = {x^2} $
The above expression can be re-written as the product of two terms giving the square of the term.
 $ 2x = x \times x $
Common factors from both the sides of the equation cancel each other.
 $ \Rightarrow 2 = x $
The above equation can be re-written as –
 $ \Rightarrow x = 2 $
Place the above value in equation (B), $ y = 2x $
 $ \Rightarrow y = 2x = 2(2) = 4 $
Hence, the required solution is $ (x,y) = (2,4) $
So, the correct answer is “ $ (x,y) = (2,4) $ ”.

Note: Common factor from the both the sides of the equation cancels each other. Be careful about the sign convention while moving any term from one side to another. While doing simplification remember the few rules. Square is the product of same number twice such as $ {n^2} = n \times n $ for Example square of $ 2 $ is $ {2^2} = 2 \times 2 $ simplified form of squared number is $ {2^2} = 2 \times 2 = 4 $ and square-root is denoted by $ \sqrt {{n^2}} = \sqrt {n \times n} $ For Example: $ \sqrt {{2^2}} = \sqrt 4 = 2 $