1/2x - 1/4y= 7/2
3/4x + 1/3y= 19/2
To change into y=, do i also multiply by 1/2 and -1/2?
on the first, multiply by -4, the second I would multlply by 3.
well when i do the intersection i am getting, (170,-354), which is not one of my answers.
To change the given system of equations into the y= form, you need to isolate the variable "y" on one side of each equation. Let's go through the process step by step for each equation.
1) 1/2x - 1/4y = 7/2
First, you want to eliminate the x term. To do this, you can multiply the entire equation by 4 to get rid of the denominators:
4 * (1/2x) - 4 * (1/4y) = 4 * (7/2)
Which simplifies to:
2x - y = 14
To isolate the variable "y":
Subtract 2x from both sides of the equation:
2x - y - 2x = 14 - 2x
This simplifies to:
-y = -2x + 14
Next, to solve for "y," you can multiply both sides of the equation by -1 to get the y term alone:
-1 * (-y) = -1 * (-2x + 14)
This simplifies to:
y = 2x - 14
So the equation 1/2x - 1/4y = 7/2 can be rewritten as y = 2x - 14.
2) 3/4x + 1/3y = 19/2
To eliminate the x term, you can multiply the entire equation by the least common multiple (LCM) of 4 and 3, which is 12:
12 * (3/4x) + 12 * (1/3y) = 12 * (19/2)
Which simplifies to:
9x + 4y = 114
To isolate the variable "y":
Subtract 9x from both sides of the equation:
9x + 4y - 9x = 114 - 9x
This simplifies to:
4y = -9x + 114
Next, divide both sides of the equation by 4 to get the y term alone:
(1/4) * (4y) = (1/4) * (-9x + 114)
This simplifies to:
y = (-9/4)x + 57/2
So the equation 3/4x + 1/3y = 19/2 can be rewritten as y = (-9/4)x + 57/2.
To summarize, to change the given system of equations into the y= form:
- For the first equation, you multiply the entire equation by 4 and then isolate the y variable.
- For the second equation, you multiply the entire equation by 12 and then isolate the y variable.