What is the value of y in rhombus LMNO
A)4
B)6
C)12
D)24

- youngnephew34

What is the value of y in rhombus LMNO
A)4
B)6
C)12
D)24

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- youngnephew34

##### 1 Attachment

- phi

try to write an equation that shows the two halves of a diagonal are equal

- youngnephew34

|dw:1440159145510:dw|

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## More answers

- youngnephew34

hold on

- youngnephew34

Y+12=6x

- phi

yes,
now write the other equation (for the other diagonal)

- youngnephew34

\[Y=3x\]

- phi

we have two equations and two unknowns (x and y are the unknowns)
do you know how to solve them?
Y+12=6x
y= 3x

- phi

one way is to use "substitution", the other way is "elimination"

- youngnephew34

For the Y+12=6x don't you suppose to subtract one side from another

- phi

in this problem, substitution works pretty well.
start with the equations:
y+12=6x
y= 3x
notice the 2nd equation says "y is the *same thing* as 3x"
we use that to replace the y in the first equation with 3x (erase the y and put in 3x instead)
can you do that?

- youngnephew34

you will substitute the 3x in to y right

- phi

what equation do you get ?

- phi

erase the y and put in 3x instead

- youngnephew34

so 3x+12=6x

- phi

yes. now we have just 1 unknown... that is good.
to solve I would start by adding -3x to both sides, like this
3x - 3x + 12 = 6x - 3x
now simplify

- phi

on the right side you have 6 x's take away 3 x's. how many x's do we have?

- youngnephew34

3x

- phi

ok, but write out the whole equation (so we don't get confused)
3x - 3x + 12 = 3x
on the right side, we have 3x's take away 3 x's

- phi

*left side

- youngnephew34

3x+12=3x

- phi

almost. 3x - 3x is not 3x

- youngnephew34

so really 12=3x

- phi

yes
last step. divide both sides by 3

- youngnephew34

x=4

- phi

the question asks for "y" not x
but from the equations we know
y= 3x
can you find y (knowing x is 4) ?

- youngnephew34

Y=4 srry bout that

- phi

no, you were correct the first time
x=4
but we can find y using
y= 3*x

- youngnephew34

so divide 4=3x

- phi

y= 3x
says y is the same thing as 3 times x
if we knew what x is (as a number) we would multiply it by 3 and we would get y (as a number)
but from the earlier steps you found x is 4
that means we can find y using that equation.
can you try?

- phi

in other words, in
y= 3*x
erase the x and put in 4 instead (because x is the same thing as 4)

- youngnephew34

Instead you would do 4x3 right

- phi

yes, but write it 4*3 (because using x for multiply is confusing... it might mean "x" the variable)

- youngnephew34

ok so 4*3=12

- phi

right,
y=3x
y=3*4
y=12
this problem took lots of steps. See if you can go over the steps, and try to understand the way we found y is 12.

- youngnephew34

so 3x+12+6x 3x-6x=3x 12/3=3/3
12/3=4
x=4
4x3=12

- phi

3x+12=6x
then add -3x to both sides
3x-3x + 12 = 6x-3x
simplify to get
0+12 = 3x
or
12=3x <-- notice we have 3x, not just 3)
4=x

- phi

then use
y=3x
when x is 4 then y = 3*4 =12

- youngnephew34

ok got it and one more to check

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