Solving the Linear Equation 3x - 2y = 3
In this article, we will solve the linear equation 3x - 2y = 3 using different methods.
Method 1: Graphical Method
To solve the equation 3x - 2y = 3 using the graphical method, we need to first graph the equation on a coordinate plane.
The graph of the equation 3x - 2y = 3 is a straight line.
Step 1: Write the equation in slope-intercept form
The equation 3x - 2y = 3 can be written in slope-intercept form as:
y = (3/2)x - (3/2)
Step 2: Graph the equation
To graph the equation, we can use the slope and y-intercept.
- Slope (m) = 3/2
- y-intercept (b) = -3/2
The graph of the equation is shown below:
Step 3: Identify the solution
From the graph, we can see that the solution to the equation 3x - 2y = 3 is where the line intersects the x-axis.
x = 1 and y = 0
Method 2: Substitution Method
To solve the equation 3x - 2y = 3 using the substitution method, we need to solve for one variable and then substitute it into the other equation.
Step 1: Solve for x
Rearrange the equation to solve for x:
x = (2y + 3)/3
Step 2: Substitute x into the equation
Substitute x into the original equation:
3((2y + 3)/3) - 2y = 3
Simplify the equation:
2y + 3 - 2y = 3
y = 0
Step 3: Find the value of x
Substitute y = 0 into the equation x = (2y + 3)/3:
x = (2(0) + 3)/3 x = 1
Method 3: Elimination Method
To solve the equation 3x - 2y = 3 using the elimination method, we need to add or subtract the equations to eliminate one variable.
Step 1: Multiply the equations
Multiply the equation 3x - 2y = 3 by 2 to eliminate the y variable:
6x - 4y = 6
Step 2: Add the equations
Add the equations to eliminate the y variable:
6x - 4y = 6 3x - 2y = 3
Add the equations:
9x = 9
Step 3: Find the value of x
Divide by 9:
x = 1
Conclusion
The solution to the linear equation 3x - 2y = 3 is x = 1 and y = 0. We can use any of the three methods - graphical, substitution, or elimination - to solve the equation.
