3x+6y=9 and 6x-5y=-33, then y=3?

Answer 1

find out x
3x+6y=9 divide by 3
x+2y=3 substract -2y
x=3-2y

SO,

6x-5y=-33 put in x value

6(3-2y)-5y=-33 multiply
18-12y-5y=-33 add y
18-17y=-33 substract 18
-17y=-51 divide by -17
y=3

phew...

Answer 2

1) 3x + 6y = 9
2) 6x - 5y =-33
To verify if y = 3, I solve the equation system by additions and substractions method:

1) 3x + 6y = 9 X (-2)
1)' -6x -12y = -18

1)' -6x -12y = -18 I add both equations
2) 6x - 5y = -33

3) -17y = -51 multiply both sides by -1/17
-1/17(-17)y = -51(-1/17)
y = 3

y =3 => 3x + 18 = 9 => 3x = -9 => x = -3

Verification: 1) 3(-3) + 6(3) = 9 => -9 + 18 = 9 => 9 = 9 ok
2) 6(-3) -5(3) = -33 => -18 -15 = -33 => -33=-33 ok

Answer : True

Answer 3

x=-y+3
6 (- y +3 ) - 5y + 33 = 0
-6y +18 -5y +33 = 0
11y = 51
y = 51 / 11

Answer 4

3x+6y=9
3x+6 * 3=9
3x+18=9
subtract 18 from both sides so 18 cancels itself out then 9-18=-9
so it's 3x=-9
divide 3 from both sides cuz u need x alone
so it's x=-3

do the same thing with the next one plug in the y and solve like a two step equation so:

6x-5y=-33
6x-5*3=-33
6x-15=-33
add 15 to both sides so 15 cancels out and -33+15=-18
so it's 6x=-18
divide 6 from both sides cuz you need x alone
so it's x=-3

Answer 5

You can also use elimination method to drop a variable by multiplying the first equation by -2 and adding it to the other equation.

- 6x - 12y = -18
6x - 5y = -33

-17y = - 51
y = 3

Answer 6

3x + 6y = 9
6x - 5y = -33

Multiply the first equation by -2 and the second equation to this result

-6x -12y = -18
6x - 5y = -33
-------------------
-17y = -51
y = 3

Answer 7

|3 6| |x| = | 9|
|6 -5| |y| = |-33|

Gaussian elimination:
|3 6 | |x| = |9 |
|0 -17| |y| = |-51|

Equivalently:
-17y = -51
3x + 6y = 9

So, yes, y = 3. Wow. Matrix math doesn't do well here.