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multiple variable equations?
if:
5x=3y+4z
and:
3x=y+3z
Then what does 5y+5z equal to in terms of x?
thanks all :]
I know I've learned this but the lack of a variable in the third equation threw me off, thanks again!
3 Answers
- HyLv 71 decade agoFavorite Answer
My idea is to treat the two equations as a pair of simultaneous equations in y and z. We solve for y and z in terms of x, and then find what 5y + 5z is.
1. Eliminate y:
First equation - 3* second:
- 4x = -5z
Hence 5z = 4x
2. Eliminate z:
3*first - 4*second:
15x - 12x = 9y - 4y + 12z - 12z
3x = 5y
Hence
5y + 5z = 3x + 4x = 7x
PS. shhrewd means "subtract second equation from first".
- shhrewdLv 61 decade ago
5x = 3y + 4z
3x = y + 3z
Add the 1st and 2nd equation
2x = 2y + z
Add the 1st and 3rd equation
7x = 5y + 5z
7x is the answer.
- Jun AgrudaLv 71 decade ago
Relative values of y in terms of x:
5x = 3y + 4z
3y = 5x - 4z
y = (5x - 4z)/3
3x = y + 3z
y = 3x - 3z
Value of z in terms of x:
5x - 4z = 3(3x - 3z)
5x - 4z = 9x - 9z
5z = 4x
z = 4/5x
Value of y in terms of x:
5x = 3y + 4z
4z = 5x - 3y
z = (5x - 3y)/4
3x = y + 3z
3z = 3x - y
z = (3x - y)/3
3(5x - 3y) = 4(3x - y)
15x - 9y = 12x - 4y
5y = 3x
y = 3/5x
Value of 5y + 5z in terms of x:
= 5(3/5x) + 5(4/5x)
= 3x + 4x
= 7x
Answer: 7x is the value of 5y + 5z.
