Question

Solve \[2x + y = 5\] and \[3x + 2y = 8\].

Answer 1

Hint: In this question we have two linear equations with two variables and we have to calculate the value of x and y. We have different methods to solve them. We can either use a substitution method i.e. find the value of x from the first equation and put it in the second equation. Then calculate x and y.

Second method is eliminating methods i.e. making the value of any one variable the same and solving it to make it zero and get the value of the other variable. Now substitute this value in any of the one equation, we get our answer.

Formula used: We are using elimination method to solve linear equations of two variables. In the given question x and y are two variables.

Complete step by step solution: 

We will use elimination method here making coefficient of y same and eliminating y from both equations.

\[2x + y = 5\]…………………………(1)

\[3x + 2y = 8\]……………………….(2)

Multiply equation (1) by 2 on both sides and subtract equation (1) and (2),

 \[4x + 2y = 10\]……………………..(3)   

(We are multiplying this equation with 2, so each term should be multiplied by two)

\[3x + 2y = 8\]……………………….(2)

(Since we are subtracting these two equations, so sign of second equation must change)

\[x{\text{ }} + {\text{ }}0{\text{ }} = {\text{ }}2\]

 OR  \[x = 2\]

Substitute this value of x in equation (1) and simplify, we get the value of y.

 \[2x + y = 5\]…..(1)

\[2 \times 2 + y = 5\]

OR    \[4 + y = 5\]

OR    \[y = 5 - 4\]

\[\therefore y = 1\]

So our desired answer is \[x = 2\] and \[y = 1\].

Note: Make sure whichever method is used to solve these types of questions, you carefully change the sign of each term. A single use of the wrong sign might lead to the wrong solution. Elimination method is much easier compared to the substitution method. Sometimes we have to add our equations and sometimes we have to subtract them. That depends on if the variable to be eliminated has the same sign or different sign.