Equation in Standard Form: 4y - 5x = 3(4x - 2y + 1)
In this article, we will explore how to convert the equation 4y - 5x = 3(4x - 2y + 1) into standard form.
What is Standard Form?
Standard form is a way of expressing linear equations in the form Ax + By = C, where A, B, and C are integers, and A is positive. This form is useful for graphing and solving equations.
Converting the Equation
Let's start by converting the given equation into standard form. We are given:
4y - 5x = 3(4x - 2y + 1)
First, we need to expand the right-hand side of the equation using the distributive property:
4y - 5x = 12x - 6y + 3
Now, let's rearrange the terms to get all the x terms on one side and all the y terms on the other side:
-5x - 12x = -6y + 4y - 3
Combine like terms:
-17x = -2y - 3
Now, let's get all the variables on one side by adding 2y to both sides:
-17x + 2y = -3
Finally, let's rearrange the terms to get the equation in standard form:
2y + 17x = -3
Conclusion
In this article, we have successfully converted the equation 4y - 5x = 3(4x - 2y + 1) into standard form, which is 2y + 17x = -3. This form is useful for graphing and solving equations.
