Question

Find two constants a and b such that the test item "Simplify a(x+2y)-b(2x-y)" will have an answer of 3x+9y. what are the constants a and b?

Answer 1

you have a(x+2y)-b(2x-y)
what do you get when you multiply a(x+2y)?

Answer 2

i will do this part for you, but you do the next
a(x+2y)=a*x+a*2y=ax+2ay

Answer 3

now multiply b(2x-y)

Answer 4

2bx-by

Answer 5

sorry correction -2bx+by

Answer 6

ok so you decided to multiply -b(2x-y) which is even better!
gj

Answer 7

so we have
ax+2ay-2bx+by right?

Answer 8

right

Answer 9

ok now we need need to get to the answer 3x+9y
so we need to put our x's together and put our y's together
so i'm just gonna move some things around k?
ax-2bx+2ay+by
is this okay with you?

Answer 10

I follow

Answer 11

ok now can i do this
x(a-2b)+y(2a+b) ?

Answer 12

dosent that equal 3x+9y

Answer 13

yes we want this to equal 3x+9y
so we want the 3 to be a-2b
and
we want the 9 to be 2a+b

so we have two equations:
a-2b=3
and
2a+b=9

do you know how to solve a system of equations?

Answer 14

Matrix elimination

Answer 15

is it 4.2 and 0,6

Answer 16

ok yes i think thats what it is called

what if we multiply the second equation by 2: 2(2a+b=9)
so the 2nd equation becomes 4a+2b=18

so we have
a -2b= 3
4a+2b=18

so what if we add the equations togehter

5a+0=21

5a=21

a=21/5

so we can find b now pluggin a into one of the above equations

Answer 17

gj chuddley :)

Answer 18

thank you very much and you were great help as well myininaya

Answer 19

:)