Question

Write two solutions of \[2x + 3y = 4\]

Answer 1

Hint: In order to find the solutions of the given linear equation there is an easy way of getting a solution by taking x equal to zero by which we get the corresponding value of y. Similarly, we can put y equal to zero to obtain the corresponding value of x. By using this method we can find the solutions of the given equation and then write them as ordered pairs.

Complete step-by-step solution:
The given equation is a linear equation with variables. A linear equation in two variables can be in different forms. But the given equation is a standard form of linear equation. The general form of a linear equation of standard is \[ax + by + c = 0\] . A linear equation in two variables has infinitely many solutions.
To find the solutions of the equation \[2x + 3y = 4\] given in the question, let’s take x equal to zero. By taking x equal to zero in the given equation we get
 \[ \Rightarrow 2\left( 0 \right) + 3y = 4\]
On multiplying zero and two the above equation will reduce to
\[ \Rightarrow 3y = 4\]
On shifting the number three to the right hand side we get
\[ \Rightarrow y = \dfrac{4}{3}\]
So from here we have found our first solution of the given equation. That is, the first solution of the equation is \[\left( {0,\dfrac{4}{3}} \right)\] .
Now let take y equal to zero in the given equation to find the second solution.
\[ \Rightarrow 2x + 3\left( 0 \right) = 4\]
On multiplying three and zero the equation will reduce to
\[ \Rightarrow 2x = 4\]
On dividing two on both sides we get
\[ \Rightarrow x = 2\]
Now we have found our second solution. The second solution of the given equation is \[\left( {2,0} \right)\] .
Hence, \[\left( {0,\dfrac{4}{3}} \right)\] and \[\left( {2,0} \right)\] are the two solutions of the equation \[2x + 3y = 4\] .

Note: Keep in mind that every linear equation with one variable has a unique solution. Remember that as there are two variables in the linear equation with two variables then that means a solution is in a pair of values, one for x and one for y which satisfy the given equation.