Question

Solve the equations $2x+3y=8$ and $x+2y=5$ to find the values of x and y.

Answer 1

Hint: Assume $2x+3y=8$ as (i) and $x+2y=5$ as (ii), find the value of $x$in terms of $y$ from equation (ii) and put the value of $x$ in the equation (i) to get the value of $x$and $y$.

Complete step by step answer:
Before proceeding with the question, we must know how to solve linear equations in two variables. Linear equations in two variables can be solved by finding the value of one variable in terms of the other variable and then putting this value in the other equation to get the value of the variable.

In this question, we have to solve the equations $2x+3y=8$ and $x+2y=5$_.

Let us first take the equation as $2x+3y=8.....(i)$.

Then, let us take the second equation as $x+2y=5.....(ii)$_.

We can get the value of x from equation (ii) in terms of $y$ as shown below,

$x=5-2y.....(iii)$

Now we can substitute the value of $x$ from equation (iii) in equation (ii). Then, we
will get,

$\therefore 2\left( 5-2y \right)+3y=8$

Opening the bracket and multiplying 2 inside, we get,

$\Rightarrow 2\times 5-2\times 2y+3y=8$

Simplifying the terms, we get,

$\Rightarrow 10-4y+3y=8$

$\Rightarrow 10-y=8$

Taking constants on the left-hand side and variable on the right-hand side we get,

$\Rightarrow 10-8=y$

$\therefore y=2$

Now, we can substitute the value of $y$ obtained above, in equation (i) to get the value of x. Then, we will get,

$\Rightarrow 2x+3\times 2=8$

$\Rightarrow 2x=8-6$

$\Rightarrow 2x=2$

$\therefore x=1$

Therefore, we have obtained the values as $x=1$ and $y=2$.


Note: We must be very careful about the signs while solving the equations. While solving the equations, be careful while taking the terms from the left-hand side to the right-hand side and vice-versa. We have solved the given linear equations in two variables using the substitution method. We can use the elimination method also to solve this question. Once, we have the values of x and y, we can then substitute in the given equations to check if they are satisfying both the equations or not.