Solve 5x + 4y = 12 for y
2007-10-10 02:37:58 · 11 answers · asked by jllanos73 2 in Science & Mathematics ➔ Mathematics
5x + 4y = 12
4y = 12 - 5x
y = 12/4 - 5/4x
y = 3 - 5/4x
2007-10-10 02:54:31 · answer #1 · answered by Dr W 7 · 1⤊ 0⤋
if you mean solve for nonegative integers x and y ... here it is :
5x + 4y = 12
4 divides 5x implies 4 divides x so, let x =4k for some nonnegative integer k.
5k + y = 3
If k>=1 a contradiction is obvious for the left hand side will be larger than 3 = right hand side. So k = 0.
Thus y = 3. and x =0.
Done.
If you allowed negative integers, then there are infinitely many solutions ... we proceed as follows... from
5k + y = 3 we get y = 3 - 5k. and x = 4k.
For any integer value of k be it positive, zero or negative, we will always get the solution in integers for x and y though one of x and y will have to be a negative integer.
In other words, the solution is:
NO solutions in positive integers x and y.
One solution for x=0, where y=3.
(x,y) = ( 4k, 3 - 5k) for all integers k. And in this case at least one of x or y will have to be negative or zero. Note that this also includes the solution (x,y) = (0,3) above... Just put k=0.
If you were just looking to mean y as ANY real number, then the solution is just,
y = ( 12 - 5x ) / 4 for any real x.
Hope this helped.
:)
2007-10-10 10:24:29 · answer #2 · answered by jonny boy 3 · 0⤊ 0⤋
5x + 4y = 12 : subtract 5x from both sides
4y = 12 - 5x : Divide each term by 4
y = 3 - 5/4 x
2007-10-10 09:42:16 · answer #3 · answered by remowlms 7 · 1⤊ 0⤋
you only have one equation there with 2 unknowns, so there will be infinitely many sets of solutions.
you can however show how the value of y depends on x, simply be rearranging the equation:
5x + 4y = 12
4y = 12 - 5x
y = 3 - (5/4)x
so whatever the x value is, y will be (3 - (5/4)x)
2007-10-10 09:41:45 · answer #4 · answered by Ian C 2 · 0⤊ 0⤋
5x + 4y = 12
Do the same operation on both sides until you get the desired result
4y = - 5x + 12 {subtract 5x}
y = - 5x/4 + 3 {divide by 4}
2007-10-10 09:43:58 · answer #5 · answered by kindricko 7 · 1⤊ 0⤋
5x + 4y = 12
4y = 12 -5x
y= (12-5x)/4
2007-10-10 09:51:26 · answer #6 · answered by slylar 2 · 0⤊ 0⤋
4y = 12 - 5x
y = 3 - ( 5 / 4 ) x
or
y = - ( 5 / 4 ) x + 3
2007-10-11 03:13:37 · answer #7 · answered by Como 7 · 0⤊ 0⤋
4y = 12 - 5x
y = 3 + (5/4)x
2007-10-10 09:40:57 · answer #8 · answered by TurtleFromQuebec 5 · 0⤊ 2⤋
What I would do is substitute a zero in for x to clear the x's adn then solve for y
5(0) + 4y = 12
4y = 12
y = 3
2007-10-10 09:41:35 · answer #9 · answered by Ms. Exxclusive 5 · 0⤊ 4⤋
you can't, atleast not as a number,
It is (12-5X)/4
2007-10-10 09:40:55 · answer #10 · answered by Greg G 5 · 0⤊ 1⤋