Question

2x - 3y = 16

3x + 2y = 11
Solve the system of equations.
A) (151 2 ,5)
B) (5,-2)
C) (5, 4)
D) (-1, -6)

Answer 1

B) (5,-2)

Explanation:

we have the equations:

`2x - 3y = 16\\3x + 2y = 11`

We multiply the first equation by 3:

`3(2x-3y=16)\\6x-9y=48`

i will call this equation 1.

and we multiply the second equation by 2:

`2(3x+2y=11)\\6x+4y=22`

i will call this equation 2.

Now we subtract equation 2 from equation 1:

`6x-9y=48\\-(6x+4y=22)`

this is:

`6x-9y=48\\-6x-4y=-22`

which gives:

`6x-9y-6x-4y=48-22\\-13y=26\\y=-2`

and now that we know that
`y=-2` we substitute this value in any of the original equations to find
`x`

using
`2x - 3y = 16`

we have:

`2x - 3(-2) = 16\\2x+6=16\\2x=16-6\\2x=10\\x=5`

so
`x=5`

the answer is
`(5, -2)` which is option B.

Answer 2

1st eq: 2x -3y =16

2nd eq: 3x +2y = 11

2(5) -3(-2) = 10+6 =16

3(5) +2(-2) = 15-4 = 11

answer is B