# math

posted by on .

2x + 3y = 78
How do i solve for x and y?

2x=78
78/2=39 so x=39

3y=78
78/3=26 so y=26

Can't be, because 2(39)+ 3(26) does not equl 78

You need TWO equations when you have TWO variables, such as x and y. It can't be done with one equation. BUT, you say, what about this post giving x as 39 and y as 26.
To determine if the first answer posted is correct, simply put the numbers back into the equation and see if the equation is satisfied.
2x + 3y = 78
2*39 + 3*26 = 78
78 + 78 = 78?? OOPS!.
So x = 39 and y = 26 isn't correct. Ya gotta have two equations. I hope this helps.

2x + 3y = 78
3x + 2y = 72

Here is the original question: Pencils have one price and pens have another. Two pencils and three pens cost 78 cents, but three pencils and two pens cost 72 cents. How much does one pencil cost?

Use variable x for pencils and y for pens.

2x + 3y = 78
3x + 2y = 72

In the first equation, solve for y.

2x + 3y = 78
3y = 78 - 2x
y = (78 - 2x) / 3

Substitute this value for y into the second equation.

Hers is another one: 3 people requires 3 weeks and 2 days to do a job. How long would it take for 4 people to do the same job? (Each week is 6 days)

48

1--2x + 3y = 78
2--Divide through by 2 yielding x + y + y/2 = 39
3--y/2 must be an integer k making y = 2k
4--Substituting, 2x + 6k = 78 making x = 39 - 3k.
5--k....0....1....2....3....4....5....6
...x...39...36...33...30...27...24...21
...y...0....2.....4...6....8....10...12

...k...7...8...9...10...11...12...13
...x..18..15..12...9....6....3....0
...y...14.16..18...20...22...24...26

65

• math - ,

-9x-13-9x=-31