Question

Find two solutions of the equation \[3x - 2y = 5\].

Answer 1

Hint:
We will use the trial-and-error method to solve the given equation. We will substitute different values of the variable in the LHS of the given equation and check which set of values give us the RHS. The solution set which satisfies the equation will be the required answer.

Complete step by step solution:
The equation given to us is \[3x - 2y = 5\].
A solution to any equation is the values of the unknown variables for which the LHS of the equation becomes equal to the RHS.
The LHS in the given equation is \[3x - 2y\].
We have to find two sets of values of \[x\] and \[y\] such that the LHS becomes equal to 5, which is the RHS. Let us find the solution by trial-and-error method.
Let us first substitute different values for \[x\] and \[y\] in the LHS of the given equation and check which values give us the RHS.
Let us put \[x = 0\] and \[y = 0\] in the LHS \[3x - 2y\]. This gives us
\[3(0) - 2(0) = 0\]
As LHS is not equal to the RHS, the solution set is incorrect.
Now, we will put \[x = 3\] and \[y = 2\] in the LHS. Therefore, we get
\[3(3) - 2(2) = 5\]
We can see that LHS is equal to the RHS, hence one of the solutions is \[(3,2)\].
We need to find another solution.
Let us put \[x = - 3\] and \[y = - 7\] in the LHS. Therefore, we get
\[3( - 3) - 2( - 7) = ( - 9) + 14 = 5\]

We can see that LHS is equal to the RHS, hence the second solution is \[( - 3, - 7)\].

Note:
The given equation is a linear equation in 2 variables. A linear equation is defined as an equation that has the highest degree of 1. There can be an infinite solution set of the given equation and we can obtain it by substituting different values of the variable in the equation. The graph of a linear equation is always a straight line.