How do you turn these equation into a standard form?
this is the standard form:
ax+by=c
here are the following equations:
2x = y + 1/2
y - 2 = 1/4x + 1
3y + 3 = 6x - 15
Please help and explain. Thank you.
1) subtract y from both sides
2) add 2 to both sides, subtract 1/4x from both sides
3)subtract 3 from both sides, subtract 6x from both sides
hope that helps
ok thank you :)
wait for the second one, which numbers would you subtract 2 from?
To convert the given equations into standard form (ax + by = c), we need to make sure that the variables (x and y) are on one side of the equation and the constants on the other side by following these steps:
1. Equation 1: 2x = y + 1/2
To start, let's move y to the left side of the equation and constants to the right side:
2x - y = 1/2
Since the coefficient of y is already -1, we don't need to make any further adjustments.
The equation in standard form is: 2x - y = 1/2
2. Equation 2: y - 2 = 1/4x + 1
To begin, let's move the x-term to the left side by subtracting 1/4x from both sides:
-1/4x + y - 2 = 1
Next, let's move the constants to the right side by adding 2 to both sides:
-1/4x + y = 3
To write the equation in standard form, we need to eliminate the fractional coefficient of x. Multiply every term in the equation by 4 to eliminate the fraction:
-4(1/4x) + 4y = 4(3)
Simplifying:
-x + 4y = 12
The equation in standard form is: -x + 4y = 12
3. Equation 3: 3y + 3 = 6x - 15
First, let's move the x-term to the left side by subtracting 6x from both sides:
-6x + 3y + 3 = -15
Next, let's move the constants to the right side by subtracting 3 from both sides:
-6x + 3y = -18
To write the equation in standard form, let's eliminate the negative coefficient of x. Multiply every term in the equation by -1 to eliminate the negative sign:
6x - 3y = 18
The equation in standard form is: 6x - 3y = 18
By following these steps, we have converted the given equations into standard form (ax + by = c).