algebra help me please! fast?

Question

10) 3x+2y=8

2y-5x=8

11)3x+3=6y

x-y=1

12) 3x=y+1

y-x=3

Answer 1

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i am assuming you are solving for x and y:

10.) 3x +2y = 8

-5x +2y = 8

since they both =8 then you can make the substitution:

3x+2y= 2y-5x

8x=0

x=0

and by putting that back in the original equ

y=4

11) 3x+3=6y is the same as -x-1=-2y (dividing both sides by -3)

and by moving it around:

-x+2y=1 and the other equ x-y=1

again they both =1 so by substitution:

-x+2y=x-y

3y=0

y=0

x=-1

12) 3x-y=1

-x +y=3

next add the bottom equ to the top one vertically to get rid of a variable

getting:

2x= 4

x=2

y=5

Answer 2

The answers with process for above questions would be like this.

10) 3x+2y=8 (equation 1)

2y-5x=8............(equation 2)

Subtracting equation 2 from 1.

3x+2y=8

2y-5x=8

- + -........Sign change indicator.

------------------------------

8x=0, so x=0.

Putting this value on equation 1 or 2 gives value of y.

so, y=4 Ans.

Now, next question is,

11) 3x+3=6y............(1)

x-y=1................(2)

Multiplying equation (2) with numerical number 3 and substracting wid eq. 1 will give solution.

3x+3=6y

3x-3y=3

- + -

------------------------

3y+3=6y-3

or, 3y=6 or, y=2 and putting that value in any equation gives value of x, so x= 3 Ans.

Now, 12) 3x=y+1............(1)

y-x=3..............(2)

Multiplying equation 2 wid 3 and adding wid equation 1.

3x=y+1

3y-3x=9

------------------

3y= y+10

2y=10, y= 5, putting that value in any equation gives value of x, so x=2 Ans.

So, whenever you are trying to find a solution for your problem like this, you could use this rule always. Seeing the situation you should decide like above about substraction and addition and the equation should be multiplied or divided to make it easy for substraction or addition which finally gives an answer easily.