Solving the Equation 3x + 2y
The equation 3x + 2y is a simple linear equation in two variables, where x and y are the variables and 3 and 2 are the coefficients. In this article, we will explore how to solve this equation and find the values of x and y.
Understanding the Equation
The equation 3x + 2y represents a straight line on a coordinate plane. The coefficients 3 and 2 determine the slope and y-intercept of the line.
- The coefficient of x, which is 3, represents the change in x over the change in y. In other words, it tells us how much x changes when y changes by 1 unit.
- The coefficient of y, which is 2, represents the change in y over the change in x. In other words, it tells us how much y changes when x changes by 1 unit.
Solving the Equation
To solve the equation 3x + 2y, we need to find the values of x and y that make the equation true. There are several methods to solve this equation, including:
- Graphical Method: We can graph the equation on a coordinate plane and find the point of intersection with the x-axis and y-axis.
- Algebraic Method: We can use algebraic manipulations to solve for x and y.
Let's use the algebraic method to solve the equation.
Algebraic Method
To solve the equation 3x + 2y, we can add or subtract the same value to both sides of the equation to isolate one variable.
For example, let's add 2y to both sides of the equation to get:
3x = -2y
Now, we can divide both sides of the equation by 3 to get:
x = -2y/3
Similarly, we can add 3x to both sides of the equation to get:
2y = -3x
Now, we can divide both sides of the equation by 2 to get:
y = -3x/2
Conclusion
The equation 3x + 2y can be solved using either the graphical method or the algebraic method. By using algebraic manipulations, we can isolate one variable and express it in terms of the other variable. The solutions to the equation are x = -2y/3 and y = -3x/2.
