Solve the system?

Question

1/3x+1/2y=5/6
1/2x-1/4y=1/4

where do i even begin?

Answer 1

Hi,

Multiply each equation by common denominator to eliminate fractions.

Multiply by 6: 1/3x+1/2y=5/6

6( 1/3x+1/2y=5/6) ==>
2x+3y=5

Multiply by 4: 1/2x-1/4y=1/4

4(1/2x-1/4y=1/4)
2x -y=1

Take these 2 equations. Multiply the first by -1 and then add.

2x+3y=5
2x -y=1

-1(2x+3y=5 )
2x -y=1

-2x -3y = -5
.2x -..y.=..1
-----------------
-4y = -4 Divide by -4 to solve for y.
y = 1

Substitute 1 for y and solve for x:

2x -y=1
2x -1=1
2x = 2
x = 1

So x = 1 and y = 1 is your answer!! I hope that helps!! :-)

Answer 2

(1) Take either equation and solve for "say" y (you can do for x also)
ex: 1/3x + 1/2y = 5/6 ------> y = 2*(5/6 -1/3x) = 5/3 - 2/3x
so, y = 5/3 - 2/3x.
take this and substitute y in second equation to solve for x.

(2) 1/2x - 1/4 (5/3 - 2/3x) = 1/4. Simplify
1/2x - 5/12 + 1/6x = 1/4 -----> 1/2x + 1/6x = 1/4 + 5/12.
Simplify....
x = 1;

(3) substitute x = 1 in y=5/3 - 2/3x ------> y = 1

I hope this helps!

Answer 3

Have you tried reading you book (really -reading- it, not just looking at the pictures) and working the example problems? That's always a good place to start.

But fhere's a hint: Multiply both sides of the top equation by 6 and both sides of the bottom equation by 4. That'll get you back to all integers instead of those terribly confusing fractions (that you didn't learn in the 4'th grade for the same reason(s) you don't seem to be learning algebra now)

HTH

Doug

Answer 4

Without solving the problem for you, you need to take one of the equations and solve for one of the variables. Once you have solved for one variable, then plug that answer into the other equation as that varable and solve. For example....

2x-4y=8
4x-2y=10

Solve for one variable in one equation...
2x-4y=8
2x=8+4y
x=4+2y
Now that you know x, plug that into the second equation...
4(4+2y)-2y=10
16+8y-2y=10
6y= -6
y= -1
Now that you know y as an integer, plug that into one equation..
x=4+2(-1)
x=2

Answer 5

1.y=3, x=2

2. X= 2, y=1

I just learned this stuff today in math and got it right away!

Answer 6

(7/4,1/2)