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
Answer:
B) (5,-2)
Step-by-step explanation:
we have the equations:
[tex]2x - 3y = 16\\3x + 2y = 11[/tex]
We multiply the first equation by 3:
[tex]3(2x-3y=16)\\6x-9y=48[/tex]
i will call this equation 1.
and we multiply the second equation by 2:
[tex]2(3x+2y=11)\\6x+4y=22[/tex]
i will call this equation 2.
Now we subtract equation 2 from equation 1:
[tex]6x-9y=48\\-(6x+4y=22)[/tex]
this is:
[tex]6x-9y=48\\-6x-4y=-22[/tex]
which gives:
[tex]6x-9y-6x-4y=48-22\\-13y=26\\y=-2[/tex]
and now that we know that [tex]y=-2[/tex] we substitute this value in any of the original equations to find [tex]x[/tex]
using [tex]2x - 3y = 16[/tex]
we have:
[tex]2x - 3(-2) = 16\\2x+6=16\\2x=16-6\\2x=10\\x=5[/tex]
so [tex]x=5[/tex]
the answer is [tex](5, -2)[/tex] which is option B.
