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brilliants [131]
3 years ago
11

What are the coordinates (x, y) at which the graphs of 2x + 3y = 12 and 2x - y = 4 intersect?

Mathematics
2 answers:
adell [148]3 years ago
5 0
A. (3,2)

3(2x-y=4)
2x+3y=12

Than cross put the y’s

8x= 24

X= 3

Than substitute the x into one of the original equations

3•2 + 3y = 12
6+ 3y = 12
-6 -6

3y = 6
/3. /3

y= 2
krok68 [10]3 years ago
3 0

Step-by-step explanation:

2x+3y=12

2x- y =4

-------------------------------------

subtraction. 4y=8

y=2

putting the value of y=2

2x-y=4

2x-2=4

2x=6

x=3

(3,2)

option A

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Consider right triangle with vertices B - base of the hill, S - top of the statue and Y - you. In this triangle angle B is right and angle Y is 13.2°. If h is a height of the statue, then the legs YB and BS have lengths 77 ft and 16+h ft.

You have lengths of two legs and measure of one acute angle, then you can use tangent to find h:

\tan 13.2^{\circ}=\dfrac{\text{opposite leg}}{\text{adjacent leg}} =\dfrac{16+h}{77}, \\ \\ 0.2345=\dfrac{16+h}{77},\\  \\ 16+h=0.2345\cdot 77=18.0565,\\ h=18.0565-16=2.0565 ft.

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