Question

CDEF is a rectangle with a width of 3 and a length of 4. One diagonal is 3x - 2y and the other diagonal is 8x + 3y. Find the values of x and y.

Answer 1

@ParthKohli @pooja195 @Michele_Laino Can one of you guys help me? Am I doing this right?

Answer 2

8x + 3y = 3x - 2y
- 2y
=1

8x + 1 = 3x
- 3x
= 5x

y = 1 x = 5 ???

Answer 3

The answer choices are...
x = 1 and y = 2
x = 1 and y = -1
x = 2 and y = 1
x = 1 and y = -2
So I know I am wrong.

Answer 4

You started right. The diagonals are equal, but you need 2 equations since you have two variables.

You can use the Pythagorean theorem/triples to find the length of the diagonal as a number

Answer 5

When I did that I got 3, 4, 5 (so 5 will be the missing triples)

Answer 6

right, so now you can write a system of equations.

\(3x-2y=5\)
\(8x+3y=5\)

Answer 7

Now I combine them into one? 3+8 = 11x + 1y = 5?

Answer 8

no. solve using elimination

Answer 9

combining into 1 won't help yet because you have 2 variables.

The y's have opposite signs, so then can be eliminated. Multiply the top equation by 3 and the bottom by 2.

Answer 10

3x - 2y = 5 * 3 = 3x - 6y = 5
8x + 3y = 5 *2 = 8x + 6y = 5
Is this right?

Answer 11

3x - 6y = 5
8x + 6y = 5
11x = 5
5 / 11 = x
x = 0.45 ?

Answer 12

not quite. Multiply the WHOLE equation (both sides)

The first equation multiplied by 3:
\[3(3x -2y) = 3(5)\]
becomes
\[9x-6y=15\]

Answer 13

What's the 2nd multiplied by 2?

Answer 14

8x + 3y = 5 *2 = 16x + 6y = 10

Answer 15

Yes. Now add the two equations