Explanations:In linear algebra, a linear equation in two variables is typically expressed in the form \(ax + by = c\), where \(a\), \(b\), and \(c\) are constants, and \(x\) and \(y\) are the variables. The coefficients \(a\) and \(b\) represent the number of units of each variable, and \(c\) is the total value. This form is used to model relationships between two variables.
For the given problem, we are told that the price of 2 balls and 1 bat is 100 units. To represent this in the form of a linear equation, we need to identify the variables and their coefficients. Let's denote the price of one ball as \(x\) and the price of one bat as \(y\).
The problem states that the total price of 2 balls and 1 bat is 100 units. This can be written as the equation \(2x + y = 100\). Here, the coefficient 2 in front of \(x\) indicates that there are 2 balls, and the coefficient 1 in front of \(y\) indicates that there is 1 bat. The total value on the right side of the equation is 100 units, which matches the given problem statement.
It is important to correctly identify the variables and their coefficients to set up the equation accurately. Misidentifying the coefficients or the total value can lead to incorrect equations. For example, if we incorrectly set up the equation as \(2x + 2y = 100\), it would suggest that there are 2 balls and 2 bats, which does not match the given problem statement. Similarly, if we set up the equation as \(x + y = 100\), it would suggest that there is 1 ball and 1 bat, which also does not match the given problem statement.
Therefore, the correct representation of the problem in the form of a linear equation is \(2x + y = 100\).