Find Values of X and Y!!!?

Question

in rectangle ABCD

AB= 2x + 6

BC= 5y

CD= 7y

DA= 2x+2

I have tried and I know that opposite sides are congruent. but when i do that i don't get an anzwer.

PLEASe Help1

Answer 1

2x+6 = 7y
-(2x+2 = 5y)
-------------------
4 = 2y
y = 2

2x+6 = 14
2x = 8
x = 4

Answer 2

Since this is a rectangle, this boils down to a "two equations / two unknowns" problem.

1) AB=CD so 2x + 6 = 7y
2) BC=DA so 2x + 2 = 5y

Solve the first equation for x (in terms of y):
x = (7y - 6)/2

Now plug this value for x into the second equation:
2((7y - 6)/2) + 2 = 5y

Then solve for the value of y:
(7y - 6) + 2 = 5y
2y = 4
y=2

With y=2, take either equation 1 or 2 above and solve for x:
1) 2x + 6 = 7y
2x + 6 = 14
2x = 8
x = 4

Is this correct? Try your values for x and y in the second equation:
2) 2x + 2 = 5y
2(4) + 2 = 5(2)
10 = 10, which is indeed true, so there is your answer (after a quick edit to my original post! *doh*!)

voila!

Answer 3

AB+BC = CD+AD
2x+6+5y = 7y+2x+2
(the 2x cancel each other out, and the 2 reduces the 6 to 4 therefore)
4+5y=7y
4=2y
Therefore y =2

Now substitute the above solution into the following equation:

AB = CD
2x+6 = 7y
2x+6 = 14
2x = 8
Therefore x = 4


Solution to above is:
y = 2
x = 4

Answer 4

I see that this rectangle is parallel with the axes...

It is a rectangle with base 4 and height (2x+6 - 7y).

Since this rectangle has base 4, then 7y - 5y, or the other way around, must also equal 4. Therefore, y = ±2.

Now, 2x+6 = 7y, so 2x+6 = ±14.

Case 1: 2x+6 = 14
2x = 8
x = 4

Case 2: 2x+6 = -14
2x = -20
x = -10

Answer 5

well, as opposite sides are congruent, AB == CD or 2x + 6 = 7y, and BC == AD or 5y = 2x + 2.

so 5y + 4 = 2x + 2 + 4 = 2x + 6 = 7y

so y = 2, and then substituting that back in to 5y = 2x + 2 you get 10 = 2x + 2 => x = 4

Where's the problem?

Answer 6

first, draw a picture. look at it. you will see that from the diagram, 2x+2=5y and 2x+6=7y. obviously then y=2, because 2y is a difference of 4. next, put the real numbers on the y sides of the rectangle and you should quickly see that x=4. then do all the math to convince your teacher you understand it.

Answer 7

If AB=DC and AD=BC, then AB=BC= CD+AD
2x+6+5y = 7y+2x+2
We then subtract 2x+2 from each side and 5y from each side to get:
4=2y
Divide by 2 to get y=2
We can then subsitute 2 for y in 7y = 2x+6
7 (2)=2x+6
14=2x+6
solve for x and you'll find X=4

Answer 8

the main nicely-known element this equation is attempting to enhance, i think of, is how order of operations works so we are going to take it in steps. a million. replace 8 for X on your equation: y = (8*2 / 4) - 2. Now remedy for y. 2. keep in mind which you do the stuff interior parenthesis first. With the stuff interior the parenthesis carry out multiplication and branch first, going from left to good. So do 8 * 2 first that's sixteen. Then divide sixteen via 4 that's 4. This leaves you with y = 4 - 2 and ... 3. y = 2. you could verify your answer via substituting 2 for y on your unique equation: 2 = (8*2/4)-2. Do the mathematics and you will discover that 2 = 2 that's real and consequently proves your answer is real. reliable luck, Amanda

Answer 9

AB=CD
2x+6=7y

BC=DA
5y=2x+2

Hence
2x+6=7/5 * (2x+2)
Multiply by 5 and use distributive property
10x+30=14x+14
14x-10x=30-14
4x=16
x=16/4=4

x=4

5y=2*4+2
5y=10
y=10/5=2

y=2

Answer 10

well, that's the key point
AB=DC
2x+6=7y 1)

AD=BC
2x+2=5y 2)

FROM 1) AND 2)

2x+6=7y
2x+2=5y

subtract one from another

2x+6=7y
-(2x+2=5y)
-------------------
2x+6=7y
-2x-2=-5y
-----------------
4= 2y
4/2= y
2=y
put the value of y in 1)
2x+6=7y
2x+6=7*2
2x+6=14
2x=14-6
2x=8
x=8/2
x=4
now check it by putting the value of x and y on their repective places. if AB=DC and AD=BC
then your answer is correct otherwise u did something wrong somewhere

Answer 11

ok!
AB=CD (opposite sides of a rectangle)
=> 2x + 6 = 7y
=> 2x - 7y = -6 --------------------(1)
also, AD = BC
=> 2x + 2 = 5y
=> 2x - 5y = -2 ----------------------(2)
therefore, subtracting (2) from (1)
2x - 7y = -6
2x - 5y = -2
(-) (+) (+)
we get, 0 - 2y = - 4
therefore y = 2
now put value of y in (1)
2x - (2) (7) = -6
2x - 14 = -6
2x = 8
x = 4
therefore,
x = 4
& y = 2