Question

$\left( 2p-1,p \right)$ is a solution of equation $10x-9y=15,$ find the value of $p.$
$\left( a \right) p=3.63$
$\left( b \right) p=5.15$
$\left( c \right) p=2.27$
$\left( d \right) p=8.45$

Answer 1

Hint: A solution of an equation is a value that always satisfies the equation. So, the given solution satisfies the equation. We will apply the solution in the equation to find the value we are asked to find.

Complete step by step solution:
Consider the given equation $10x-9y=15.$
Consider the fact that we are given a solution of the equation.
A function or a value is said to be a solution of an equation if the function or value satisfies the equation.
Since we are given with a solution, we can use that to find the value we are asked to find.
The given solution is $\left( 2p-1,p \right)$ in which $2p-1$ is the $x-$coordinate and $p$ is the $y-$coordinate.
Since $\left( 2p-1,p \right)$ is a solution of the given equation, it will satisfy the equation.
So, to find the value of $p,$ we can apply $\left( 2p-1,p \right)$ in the given equation.
Then the given equation $10x-9y=15$ will become $10\left( 2p-1 \right)-9p=15.$
Let us take $10$ inside and open the bracket on the left-hand side of the equation to get the following, $20p-10-9p=15.$
Let us transpose $10$ from the left-hand side to the right-hand side of the equation. Since $10$ is getting subtracted on the left-hand side, it will get added on the right-hand side.
So, we will get, $20p-9p=15+10=25.$
This will give us $11p=25.$
Now, we will transpose $11$ from the left-hand side to the right-hand side of the equation to get $p=\dfrac{25}{11}=2.27.$
Hence the value of $p$ is $2.27.$

Note: We have to remember that the solutions of an equation always satisfy the equation. It is possible to find the value of the solutions by applying them directly in the equation. We can find the value of the $x-$coordinate, $2p-1=3.5454.$