# In rhombus ABCD, diagonals AC and BD intersect at M. If AM=x+ 3y, BM=x+ 6, Mc= 3x- 9, and DM =2y +8, how do you find the values of x and y?

Nov 18, 2016

Values of $x = 12 \mathmr{and} y = 5$

#### Explanation:

The diagonals of a rhombus bisect each other. This means that they cut each other in half.

So $A M = C M \mathmr{and} B M = D M \therefore A M = C M \mathmr{and} x + 3 y = 3 x - 9 \mathmr{and} 2 x - 3 y = 9 \left(1\right)$
$B M = D M \mathmr{and} x + 6 = 2 y + 8 \mathmr{and} x - 2 y = 2 \left(2\right)$

Multiplying equation(2) by 2 and then subtrating from equation (1) we get , $2 x - 3 y = 9 \left(1\right)$
$2 x - 4 y = 4 \left(2\right)$
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$y = 5 \therefore x = 2 y + 2 = 10 + 2 = 12$

Values of $x = 12 \mathmr{and} y = 5$ [Ans]