If 2m - n = 3p and 2m - 5p - n = 14, what is the value of p?
Take 1st equation 2m-3p-n=0
Take 2nd equation 2m-5p-n=14
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now exchnage signs of the 2nd equation and do adition with changed signs.
2m -3p -n= 0
2m -5p -n= 14
(-) (+) (+) (-)
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2p = -14
p = -7
value of p is -7
To find the value of p, we will use the given equations and solve them simultaneously.
Given:
1) 2m - n = 3p
2) 2m - 5p - n = 14
Let's solve these equations step by step:
Step 1: Simplify equation 2 by rearranging the terms:
2m - n - 5p = 14
Step 2: Subtract equation 1 from equation 2:
(2m - n - 5p) - (2m - n) = 14 - 3p
Simplifying further:
2m - n - 5p - 2m + n = 14 - 3p
-5p + 3p = 14
-2p = 14
p = -14/2
p = -7
Therefore, the value of p is -7.
To find the value of p, we will use the given equations to solve for p.
The equations are:
2m - n = 3p ...(Equation 1)
2m - 5p - n = 14 ...(Equation 2)
We can use Equation 1 to express p in terms of m and n.
Rearranging Equation 1, we get:
3p = 2m - n
Dividing both sides by 3, we have:
p = (2m - n)/3 ...(Equation 3)
Now, substitute Equation 3 into Equation 2 to get the value of p:
2m - 5((2m - n)/3) - n = 14
Multiply both sides of the equation by 3 to eliminate the fraction:
6m - 10(2m - n) - 3n = 42
Expand the equation:
6m - 20m + 10n - 3n = 42
Combine like terms:
-14m + 7n = 42
Now, we have an equation involving only m and n.
To solve this equation, we need more information or another equation involving m and n. If you have any additional equations or further information, please provide them so that we can continue solving for the value of p.