Find the substitution 2x+3y=-5 and y=-x+5

Mathematics

1 answer:

tatuchka [14]2 years ago

3 0

Answer: x = 20, y = -15

Step-by-step explanation:

Since we already know that $y=-x+5$ , we can just substitute in that value of y into the other equation:

$2x+3y=-5\\2x+3(-x+5)=-5\\2x-3x+15=-5\\-x=-5-15\\-x=-20\\x=20$

with the value of x, we can find the value of y:

$y=-x+5=-20+5=-15$

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(b)39 degrees

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Plane X with an average speed of 50km/hr travels for 2 hours from P (Kano Airport) to point Q in the diagram.

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Therefore: PQ =50km/hr X 2 hr =100 km

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Using alternate angles in the diagram:

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(a)First, we calculate the distance traveled, PA by plane Y.

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$q^2=p^2+a^2-2pa\cos Q\\q^2=100^2+125^2-2(100)(125)\cos 110^\circ\\q^2=34175.50\\q=184.87$ km$

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Therefore:

Average Speed of Y

$=184.87 \div 1.5\\=123.25$ km/hr\\\approx 123$ km/hr (correct to three significant figures)$

(b)Flight Direction of Y

Using Law of Sines

$\dfrac{p}{\sin P} =\dfrac{q}{\sin Q}\\\dfrac{125}{\sin P} =\dfrac{184.87}{\sin 110}\\123 \times \sin P=125 \times \sin 110\\\sin P=(125 \times \sin 110) \div 184.87\\P=\arcsin [(125 \times \sin 110) \div 184.87]\\P=39^\circ $ (to the nearest degree)$