Find the values of x and y.

Mathematics

1 answer:

vova2212 [387]2 years ago

4 0

Look at the picture.

We have the equation (1) 12x + 4y = 40.

We know, the sum of the acute angles in a right triangle is 90°.

Therefore we have the equation (2) (12x + 4y) + (17x - y) = 90

Substitute (1) to (2):

40 + 17x - y = 90 subtract 40 from both sides

17x - y = 50 (3)

We have the system of equations:

$\left\{\begin{array}{ccc}12x + 4y = 40&|:4\\17x-y=50\end{array}\right\\\underline{+\left\{\begin{array}{ccc}3x + y = 10\\17x-y=50\end{array}\right}\ \text{add both side of equations}\\.\qquad20x=60\qquad|:20\\.\qquad x=3$

Substitute the value of x to (3)

$17(3)-y=50\\51-y=50\qquad|-51\\-y=-1\to y=1$

Answer: x = 3 and y = 1.

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