Question

Write the solution of the pair of the linear equations 4x + 2y = 5 and x –2 y = 0.

Answer 1

Hint: Use one of the equations from the question to express x in terms of y. Substitute x in the other equation and solve it to reach the answer.

Complete step-by-step answer:
Before starting with the solution, let us discuss the significance of linear equations Linear equations in two variables represent the equation of a line on the x-y plane. The solution to two linear equations in two variables represents the meeting point of the two lines represented by the equations.
Now we will move to the solution to the given question. First, let us begin with the equation x-y=0.
$\therefore x-2y=0$
Now we will take 2y to the other side of the equation to express x in terms of y.
x =2 y……………….(i)
Now we will substitute the value of x from equation (i) to the other equation given in the question. On doing so, we get
4x + 2y = 5
$\Rightarrow 4\times 2y+2y=5$
$\Rightarrow y=\dfrac{5}{10}=\dfrac{1}{2}$
And as from equation (i) we know x is equal to 2y, so, we can say that x = $2\times \dfrac{1}{2}=1$ .
Therefore, the solution of the linear equation given in the question is $\left( 1,\dfrac{1}{2} \right)$ .

Note: Be careful with the signs and calculations as in such questions, the possibility of making a mistake is either of the sign or a calculation error. Always represent the solution of two linear equations in two variables in the form of (x,y) as the solution is the meeting point of the two lines represented by the linear equations.