# Solving this linear system

#### Stine

##### New member
1/2x-3/5y=2

4/5x+9/2y=3/10

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

=23/5= 3.333 repeating

I know there are such things as ugly numbers but I have to do some plugging here somewhere don't I?????? OH... Please help me! #### arthur ohlsten

##### Full Member
eq1)
1/2 x - 3/5 y =2 to clear fractions multiply both sides by 10
5x -6y=20

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eq2)
4/5 x 9/2 y =3/10 multiply both sides by 10
8x+45y=3

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solve 2 equations in 2 unknowns

5x-6y=20
8x+45y=3

I will solve this by one method but you use the technique you are being taught

multiply first equation by 15, and second by 2
75x-90y=300
16x+90y=6
91x=306
x = 91/306
factors 91 = 1,7,13 none are factors of 306 except 1

x=91/306 answer can't be reduced

to find y multiply first equation by -8 and second by 5
-40x+48y=-160
40x+225y=15
273y=-145
y=-145/273

factors of 145=1,5,29none of which are factors of 273

Arthur

#### Denis

##### Senior Member
Stine said:
> 1/2x-3/5y=2
> 4/5x+9/2y=3/10

Much easier if you rewrite such equations this way:
x / 2 - 3y / 5 = 2
4x / 5 + 9y / 2 = 3 / 10

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

No idea what you're trying to do;
you have to COMBINE the 2 equations in order to solve :shock:

#### arthur ohlsten

##### Full Member
I did solve the 2 equations. The first steps I took were to change the equations to have integer coefficients, rather than fractions. This is not neccessary, but I find it convenient.
Arthur

#### Denis

##### Senior Member
Hey Arthur, my post is adressed to Stine; NOT commenting on yours #### arthur ohlsten

##### Full Member
Sorry,I misunderstood.

let the total be 129.6 pineapples,then you can have the fourth man take 1/4 of the total

man no...........amount taken..........amount left
1,,,,,,,,,,,,,,,,,,,,,,,,,43.2,,,,,,,,,,,,,,,,,,,,,,, 86.4
2,,,,,,,,,,,,,,,,,,,,,,,,28.8,,,,,,,,,,,,,,,,,,,,,,,,,,57.6
3,,,,,,,,,,,,,,,,,,,,,,,19.2,,,,,,,,,,,,,,,,,,,,,,,,,,,38.4
4,,,,,,,,,,,,,,,,,,,,,,,, 32.4,,,,,,,,,,,,,,,,,,,,,,,,,,,6

Arthur