# Solve for x and y by using method of substitution:

$0.2x + 0.3y = 1.3,{\text{ }}0.4x + 0.5y = 2.3$

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Hint – In this question there are given two equations involving two variables x and y. Use a method of substitution to find out the value of these two variables. In this method we try to find the value of any variable from any equation and put this value into another equation so, use this concept to reach the solution of the question.

Complete step by step solution:

Given equations

$0.2x + 0.3y = 1.3,{\text{ }}0.4x + 0.5y = 2.3$

Now multiply by 10 in given equations we have

$2x + 3y = 13$………………… (1)

$4x + 5y = 23$…………………………. (2)

Now use Substitution method to solve these equations

So, from equation (1) calculate the value of y we have,

$ \Rightarrow 3y = 13 - 2x$

Now divide by 3 we have,

$ \Rightarrow y = \dfrac{{13 - 2x}}{3}$

Now put this value of y in equation (2) we have,

$ \Rightarrow 4x + 5\left( {\dfrac{{13 - 2x}}{3}} \right) = 23$

Now simplify the above equation we have,

$ \Rightarrow 12x + 65 - 10x = 69$

$ \Rightarrow 2x = 4$

$ \Rightarrow x = 2$

Now substitute the value of x in equation (1) we have,

$ \Rightarrow 2 \times 2 + 3y = 13$

Now simplify the above equation we have,

$ \Rightarrow 3y = 13 - 4 = 9$

$ \Rightarrow y = \dfrac{9}{3} = 3$

So, x = 2 and y = 3 is the required solution of the equation.

Note – Whenever we face such types of problems the key concept is to use various methods of variable evaluation either by elimination or by substitution method. These methods will help in getting the right track to evaluate these equations involving two variables and reach the right solution.

Complete step by step solution:

Given equations

$0.2x + 0.3y = 1.3,{\text{ }}0.4x + 0.5y = 2.3$

Now multiply by 10 in given equations we have

$2x + 3y = 13$………………… (1)

$4x + 5y = 23$…………………………. (2)

Now use Substitution method to solve these equations

So, from equation (1) calculate the value of y we have,

$ \Rightarrow 3y = 13 - 2x$

Now divide by 3 we have,

$ \Rightarrow y = \dfrac{{13 - 2x}}{3}$

Now put this value of y in equation (2) we have,

$ \Rightarrow 4x + 5\left( {\dfrac{{13 - 2x}}{3}} \right) = 23$

Now simplify the above equation we have,

$ \Rightarrow 12x + 65 - 10x = 69$

$ \Rightarrow 2x = 4$

$ \Rightarrow x = 2$

Now substitute the value of x in equation (1) we have,

$ \Rightarrow 2 \times 2 + 3y = 13$

Now simplify the above equation we have,

$ \Rightarrow 3y = 13 - 4 = 9$

$ \Rightarrow y = \dfrac{9}{3} = 3$

So, x = 2 and y = 3 is the required solution of the equation.

Note – Whenever we face such types of problems the key concept is to use various methods of variable evaluation either by elimination or by substitution method. These methods will help in getting the right track to evaluate these equations involving two variables and reach the right solution.

Last updated date: 20th Sep 2023

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