Solving the Equation: 3x + 2y = 5
In this article, we will solve the linear equation 3x + 2y = 5. We will go through the steps to find the values of x and y that satisfy the equation.
Understanding the Equation
The equation 3x + 2y = 5 is a linear equation in two variables. The equation has two variables, x and y, and two coefficients, 3 and 2. The constant term is 5.
Solving the Equation
To solve the equation, we can use different methods, such as substitution, elimination, or graphing. Here, we will use the substitution method.
Step 1: Choose a Variable
Let's choose x as the variable to solve for. We can do this by isolating x on one side of the equation.
Step 2: Isolate x
To isolate x, we can subtract 2y from both sides of the equation.
3x + 2y = 5 3x = 5 - 2y
Step 3: Divide by 3
Now, we can divide both sides of the equation by 3 to get x in terms of y.
x = (5 - 2y) / 3
Step 4: Find the Value of y
To find the value of y, we can plug in a value for x and solve for y. Let's say x = 1.
1 = (5 - 2y) / 3 3 = 5 - 2y 2y = 5 - 3 2y = 2 y = 1
Step 5: Find the Value of x
Now that we have the value of y, we can find the value of x.
x = (5 - 2(1)) / 3 x = (5 - 2) / 3 x = 3 / 3 x = 1
Answer
The solution to the equation 3x + 2y = 5 is x = 1 and y = 1.
Conclusion
In this article, we have solved the linear equation 3x + 2y = 5 using the substitution method. We have found the values of x and y that satisfy the equation, which are x = 1 and y = 1.
