5x/3+y=c
2y=c-4x
x+y=6
What is c? I've tried substituting y as x-6 however I'm still not getting it.
let's clear fractions and see what we have
5x+3y=3c
4x+2y=c
x+y=6
If we subtract the 2nd from the 1st we have
x+y=2c
x+y=6
that help?
To find the value of c, we can use the given system of equations:
1) 5x/3 + y = c
2) 2y = c - 4x
3) x + y = 6
Let's solve this step by step:
First, we need to eliminate the variable c from equations 1 and 2. To do this, we can use the second equation and solve for c:
2y = c - 4x
Rearranging the equation, we get:
c = 2y + 4x
Now we can substitute this value of c into equation 1:
5x/3 + y = 2y + 4x
Next, let's simplify the equation:
5x/3 - 4x + y - 2y = 0
Combining like terms:
(5x - 12x + 3y - 6y)/3 = 0
(-7x - 3y)/3 = 0
To eliminate the fraction, we can multiply both sides of the equation by 3:
-7x - 3y = 0
Now, we have equation 4:
-7x - 3y = 0
Let's solve equations 3 and 4 simultaneously:
x + y = 6
-7x - 3y = 0
To eliminate x, let's multiply equation 3 by 7:
7x + 7y = 42
Now, we can add equations 7 and 4:
7x + 7y + (-7x - 3y) = 42 + 0
Simplifying further:
4y = 42
Now, solving for y:
y = 42/4
y = 10.5
Finally, we can substitute the calculated value of y back into equation 3 to find x:
x + 10.5 = 6
x = 6 - 10.5
x = -4.5
So, the solution to the system of equations is x = -4.5, y = 10.5.
Now, let's find the value of c by substituting the values of x and y into equation 2:
2y = c - 4x
2(10.5) = c - 4(-4.5)
21 = c + 18
c = 21 - 18
c = 3
Therefore, the value of c is 3.