(math) a highschool problem! ( show work )?

Question

3y = 5x + 15
6x = 2y - 18
_________
Help!
( show your work )

Answer 1

Ok, let's go on_

3y - 5x = 15

6x - 2y = -18

Let's multiply the first equation by 2, and the second equation by 3

6y - 10x = 30

18x - 6y = -54

8x = -24

x = -3

replacing x = -3 on the first equation : y = 0


Hope that helps

Answer 2

from the second equation
6x + 18 = 2y
divide both sides by 2
3x + 9 = y
plug in the value of y in the first equation
3 (3x + 9) = 5x + 15
9x + 27 = 5x + 15
9x - 5x = 15 - 27
4x = -12
x = -3

Plug in value of x in any of the two original equations to get the value of y. From the first equation:

3y = 5 (-3) + 15
3y = -15 + 15
3y = 0
y = 0

Answer 3

3y = 5x + 15
6x = 2y - 18

Method 1 :- (Called Substitution method)
----------------
3y = 5x + 15
y = (5x + 15)/3

Substitute value of y in first eqn
6x = 2y - 18
6x = 2(5x + 15)/3 - 18
6x = (10x + 30)/3 - 18
6x = 10x/3 + 30/3 - 18
6x = 10x/3 + 10 - 18
6x - 10x/3 = 10 - 18
(18x - 10x)/3 = -8
8x = -8 * 3
8x = -24
x = -24/8
x = -3

Substitute value of x back in any equation.
3y = 5x + 15
3y = 5(-3) + 15
3y = -15 + 15
3y = 0
y = 0/3
y = 0

Hence x = -3, y = 0


Method 2 :- (Called Addition of both equations)
-----------------
Take each equation at a time :-
3y = 5x + 15
3y - 15 = 5x
-15 = 5x - 3y
i.e.
5x - 3y = -15

6x = 2y - 18
6x - 2y = -18

Now,
5x - 3y = -15 - eqn 1
6x - 2y = -18 - eqn 2

Try to make one of the co-efficients of x or y in both equations as equal.
Here, I choose 'y'.

2 * eqn 1 :-
2(5x - 3y) = 2*-15
10x - 6y = -30

3 * eqn 2 :-
3(6x - 2y) = 3*-18
18x - 6y = -54

Now both equations have become
10x - 6y = -30 - eqn 3
18x - 6y = -54 - eqn 4

Now the co-efficient of 'y' in both equations is -6.

Change all signs of eqn 3, this becomes,
-10x + 6y = +30 -eqn 3
18x - 6y = -54 - eqn 4

"Adding both equations" :-
Each variable is to be added with its counterpart
i.e. add x of eqn 1 with x of eqn 2 and y of eqn 1 with y of eqn 2, etc ...
-10x + 18x + 6y - 6y = + 30 - 54
As '6y-6y' gets removed, just solve the rest to get :-
8x = -24
x = -24/8
x = -3

Substitute the value of x in any equation.
Lets take the first equation :-
3y = 5x + 15
3y = 5(-3) + 15
3y = -15 + 15
3y = 0
y = 0

Hence x = -3, y = 0

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Now, Its better to understand both methods and use any one method in your problems for your homework. Try to understand any one of the methods rather than just using the answer here. I know I'm helping you with homework. But its better to understand than expect answers from people. Once you do it yourself, You can even do it in your sleep. You have to get the method and such kind of problems with such questions will be a thing of the past.

Answer 4

Realign your equations so they are in the form
-5 x + 3y = 15 eq A
6x -2y = 18 eq B

Multiply equation A by 3
Multiply equation B by 2
Add the two multiplied equations. The y-terms should cancel out, leaving -3x = C, where C is the term on the right-hand side. Then x= - C/3
Now go back to equation A or B, and substitute in the value of x you attained (carefully!). Then you can calculate the value of y.

Answer 5

3y - 5x - 15 = 0
-2y + 6x +18 = 0

multiply line 1 by 2 and, line 2 by 3
6y - 10x -30 = 0
-6y + 18x + 54 = 0

add lines together

8x + 24 = 0
x = -3

sub into 1st line
3y - 5(-3) - 15 = 0
3y = 0
y = 0

Answer 6

Always make it easy . . . 1. Which of the following open sentences is true for all real numbers x? Make it easy by looking at simplest first (b) |7-x|>0 not true if x=7 (c) is pretty straight forward. You can solve it for a unique value of x, so it is not true for ALL values of x. (a) can be factored - so lets see what happens there: 3[x-5](2-x)]=2(9x+15) 3[x-5](2-x)]=2*3(3x+5) ½[x-5](2-x)]=(3x+5) Not a true statement if I let x=5 0 ≠(3*5 + 5) Must be (D) 4. - just plug-in your point values for x (x=1,y=3) and (-2,0): a) y=x^2+3 x=1, y=4 nope b) y=x^2+4 x=1, y=5 nope c) y=x^2-4 x=1, y=-3 nope d) y=-x^2+4 x=1, y=3 yes x= -2, y=0 YES!!

Answer 7

3y=5y+15 / substract 15
6x=2y-18 / add 18
--
5x+15-3y=0 /substract 15
2y-18-6x=0 / add 18
--
5x-3y=-15 / * by 2
-6x+2y=18 / * by 3
--
10x-6y=-30
-18+6y=54
_________
-8x= 24
x = -3
--
5x-3y=-15
5*(-3)-3y=-15
-15-3y=-15
-3y=0
y=0

Answer 8

you can use sub. rule- but first you can reduce the second equation to 3x=y-9 looking at equation two, try to move eveything on one side, leaving y all alone.
it will then be 3x+9=y
then plug this into the first equation
3(3x+9)=5x+15
9x+27=5x+15
4X =-12
x=-3

Answer 9

3y = 5x +15
6x = 2y - 18

18y = 30x + 90 ---------> Multiply by 6
30x = 10y - 90 ---------> Multiply by 5

18y = 30x + 90 -------> We know 30x = 10y - 90
So
18y = (10y - 90 ) + 90
18y = 10y
8y = 0
y = 0

So, when y=0
6x = 2y - 18
6x = 2(0) - 18
6x = -18
x = -3
So the answer is
(-3,0)

Answer 10

do your own homework