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Solving Equations
- Thread starter tina1116
- Start date
tina1116 said::?:
I have to solve for z:
4z-3y=8
when I checked my answer in the book it gave me z=3/4 +2
How did it become a fraction and where did the two come from :?: :?:
The original equation is 4z - 3y = 8 We solve this for z just as we would any equation: move all terms that do not have z to the other side, leaving 4z alone on the left-hand side of the equation.
4z = 3y + 8
Now divide both sides of the equation by 4.
If the answer you gave, z = 3/4 + 2, came from your textbook, it's wrong, as y has been left out.
I have to solve for z:
4z-3y=8
when I checked my answer in the book it gave me z=3/4 +2
How did it become a fraction and where did the two come from
The expression ax + by = c, "a" and "b" relatively prime, "c" > a(b), has positive integer solutions if d = g.c.d.(a,b) divides "c". If the g.c.d.(a,b) = d, d must divide c evenly for integral solutions.
1--Given 4y - 3z = 8
2--Divide through by the lowest coefficient yielding1y + y/3 - z = 2 + 2/3
3--(y - 2)/3 must be an integer k making y = 3k + 2
4--Substituting back into (1) yields 12k + 8 - 3z = 8 making z = 4k.
5--k can be any positive integer from 1 on up
6--k.....0.....1.....2.....3.....4.....5.....6.....7
....y.....2.....5.....8....11...14....17...20...23...........
....z.....0.....4.....8....12...16....20...24...28..........
Thus, z can be any positive integer depending on the value of y.
To have z = 2 3/4, y would have to be 4 1/16.
4z-3y=8
when I checked my answer in the book it gave me z=3/4 +2
How did it become a fraction and where did the two come from
The expression ax + by = c, "a" and "b" relatively prime, "c" > a(b), has positive integer solutions if d = g.c.d.(a,b) divides "c". If the g.c.d.(a,b) = d, d must divide c evenly for integral solutions.
1--Given 4y - 3z = 8
2--Divide through by the lowest coefficient yielding1y + y/3 - z = 2 + 2/3
3--(y - 2)/3 must be an integer k making y = 3k + 2
4--Substituting back into (1) yields 12k + 8 - 3z = 8 making z = 4k.
5--k can be any positive integer from 1 on up
6--k.....0.....1.....2.....3.....4.....5.....6.....7
....y.....2.....5.....8....11...14....17...20...23...........
....z.....0.....4.....8....12...16....20...24...28..........
Thus, z can be any positive integer depending on the value of y.
To have z = 2 3/4, y would have to be 4 1/16.