Question

Solve the following - \[x+7y=10;3x-2y=7\]

Answer 1

Hint: For solving this question you should know about the general mathematical calculation of expressions. In this problem it is asked to find the values of x and y. And this can be solved by general addition and submission of any numbers or terms on both sides. As we can say any term is added or subtracted as a form of zero or by adding to both.

Complete step by step solution:
According to our question it is asked to us to find the value of x, y if the equation is –
\[x+7y=10-\left( 1 \right);3x-2y=7-\left( 2 \right)\]
Now, as we know that if we want to solve any equation or any expression then we can add any term as a form of zero. It means that there will be addition and submission of the same term with the same signs if we are adding or subtracting that from both sides of an equation. And if we add in only one side of the equation then we add and subtract the same term with one negative and one positive sign.
So, if we want to solve our question then we will add -7y in both sides of equation (1): -
\[\begin{align}
  & x+7y-7y=10-7y \\
 & x=10-7y-\left( 3 \right) \\
\end{align}\]
Now, put this value of x in equation (2)
\[\begin{align}
  & \Rightarrow 3\left( 10-7y \right)-2y=7 \\
 & \Rightarrow 30-21y-2y=7\Rightarrow 23y=23\Rightarrow y=1 \\
\end{align}\]
And put the value of y in equation (3)
\[\Rightarrow x=10-7\left( 1 \right)=3\]
So, the values of x and y are 3 and 1 respectively.

Note: While solving this type of question we have to always add or subtract the term which will make the question easy. And if the variables are of higher order than too. We will make the higher ordered term to add or subtract in the equation.