how do i turn the following equations into standard form?
-14x = 24 + 18y
y = 9/2x - 7/2
-3y = -6 + 6x
-20/3 = 5y + -5x
y = 3/2x + 5
standard form is ax+by=c. so just plug them all into that form. for example, the first one would be -14x-18y=24. you have to change the sign of 18 because you move it to the other side of the equation.
Because you are dealing with equations, to keep them equal, whatever you do to one side, you have to do to the other. To get rid of the 18y on the right side, you have to subtract 18y from both sides. Use the same principle on the remaining equations.
I hope this helps a little more. Thanks for asking.
To convert these equations into standard form, we need to rearrange the equations so that they follow the general form Ax + By = C, where A, B, and C are constants.
1. -14x = 24 + 18y
We can start by moving all the terms to one side of the equation.
-14x - 18y = 24
Now, we can multiply both sides of the equation by -1 to make the coefficient of x positive.
14x + 18y = -24
This is now in standard form.
2. y = (9/2)x - 7/2
We can start by multiplying both sides of the equation by 2 to eliminate the fraction.
2y = 9x - 7
Next, we can rearrange the equation to have x and y terms on one side and a constant on the other side.
-9x + 2y = -7
This is now in standard form.
3. -3y = -6 + 6x
We can start by moving all the terms to one side of the equation.
-3y - 6x = -6
Next, we can multiply both sides of the equation by -1 to make the coefficient of y positive.
3y + 6x = 6
This is now in standard form.
4. -20/3 = 5y + -5x
We can start by multiplying both sides of the equation by 3 to eliminate the fraction.
-20 = 15y - 15x
Next, we can move all terms to one side of the equation.
15x - 15y = -20
We can divide both sides of the equation by -15 to simplify the coefficients.
x - y = 4/3
This is now in standard form.
5. y = (3/2)x + 5
We can start by rearranging the equation to have x and y terms on one side and a constant on the other side.
- (3/2)x + y = 5
Next, we can multiply both sides of the equation by 2 to eliminate the fraction.
-3x + 2y = 10
This is now in standard form.