Solving the Equation: 3a + 2b
In algebra, solving equations is a fundamental concept that helps us find the values of unknown variables. One such equation is 3a + 2b, which can be solved using various methods. In this article, we will explore the solution to this equation and understand the underlying concepts.
What is the Equation 3a + 2b?
The equation 3a + 2b is a linear equation with two variables, a and b. The equation can be read as "three times a plus two times b." The coefficients of the variables are 3 and 2, respectively.
How to Solve the Equation 3a + 2b
To solve the equation 3a + 2b, we need to find the values of a and b that make the equation true. Since there are two variables, we need two equations to solve for both variables. Let's assume we have another equation, say, 2a - 3b = 5.
We can use the method of substitution or elimination to solve the system of equations. Here, we will use the substitution method.
Step 1: Solve one of the Equations for one Variable
Let's solve the second equation for a:
2a - 3b = 5 2a = 5 + 3b a = (5 + 3b) / 2
Step 2: Substitute the Expression into the other Equation
Substitute the expression for a into the first equation:
3a + 2b = ? 3((5 + 3b) / 2) + 2b = ?
Step 3: Simplify and Solve
Simplify the equation:
(15 + 9b) / 2 + 2b = ? 15 + 9b + 4b = ? 13b = -15
Now, solve for b:
b = -15 / 13
Step 4: Find the Value of the Other Variable
Substitute the value of b back into one of the original equations to find the value of a:
a = (5 + 3(-15 / 13)) / 2 a = (5 - 45 / 13) / 2 a = (65 - 45) / 26 a = 20 / 26 a = 10 / 13
Therefore, the solution to the equation 3a + 2b is a = 10 / 13 and b = -15 / 13.
Conclusion
In this article, we solved the equation 3a + 2b using the substitution method. By following the steps, we were able to find the values of a and b. This solution can be verified by plugging the values back into the original equation. Solving equations like 3a + 2b is essential in algebra and has numerous applications in physics, engineering, and other fields.
