Question

Write 3 solutions of the following equation: \[2x - y = 3\].

Answer 1

Hint:
Here, we will use the concept of substitution to find all the solutions. We will substitute different values of \[x\] in the equation and solve it to get different values of \[y\]. All the pairs of \[x\] and \[y\] that satisfy the equation \[2x - y = 3\] are the solutions of the equation.

Complete step by step solution:
The given equation is a linear equation in two variables. A linear equation in two variables has infinitely many solutions.
We can substitute different values of \[x\] in the equation and solve it to get different values of \[y\]. There are infinite values of \[x\] that we can substitute.
Now, we will substitute the value \[x = 0\] in the given equation.
\[2 \cdot 0 - y = 3\]
Now, multiplying the terms, we get
\[0 - y = 3\]
We will solve this equation further to get the value of \[y\] when \[x = 0\].
\[y = - 3\]
Hence, one solution of the equation \[2x - y = 3\] is \[x = 0\] and \[y = - 3\], that is \[\left( {0, - 3} \right)\].
Next, we will substitute the value \[x = 1\] in the given equation.
\[2 \cdot 1 - y = 3\]
Now, multiplying the terms, we get
\[2 - y = 3\]
We will solve this equation further to get the value of \[y\] when \[x = 1\].
\[y = - 1\]
Hence, one solution of the equation \[2x - y = 3\] is \[x = 1\] and \[y = - 1\], that is \[\left( {1, - 1} \right)\].
Now, we will substitute the value \[x = 2\] in the given equation.
Thus, we get
\[2 \cdot 2 - y = 3\]
Now, multiplying the terms, we get
\[4 - y = 3\]
We will solve this equation further to get the value of \[y\] when \[x = 2\].
\[y = 1\]
Hence, one solution of the equation \[2x - y = 3\] is \[x = 2\] and \[y = 1\], that is \[\left( {2,1} \right)\].

Therefore, we get the three solutions of \[2x - y = 3\] as \[\left( {0, - 3} \right)\], \[\left( {1, - 1} \right)\], and \[\left( {2,1} \right)\].

Note:
A linear equation is an equation in which each variable has the highest power of one. A linear equation can have one, two or even three variables. The equation provided to us is a linear equation in two variables. Here, the value of \[x\] is not provided to us, so we can arbitrarily choose any value of \[x\] to find the corresponding value of \[y\]. There are infinite values of \[x\] that we can substitute. Therefore, there are infinite solutions of a linear equation in two variables that we can find.