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3 years ago

2x+3y=13 4x-y=2 solve the simaltaneous equation

Mathematics

1 answer:

nekit [7.7K]3 years ago

5 0

Solve by substitution. We begin by manipulating the second equation (solving for y).

2x+3y=13

4x-y=-2 => -y=-4x-2 => y=4x+2

Now substitute "4x+2" for y into the first equation because y=4x+2.

2x+3y=13 becomes 2x+3(4x+2)=13

Now solve for x.

2x+3(4x+2)=13

2x+12x+6=13

14x=7

x=1/2

Now we can solve for y because we know what x is.

y=4x+2 => y=4(1/2)+2 = y=4

answer: x=1/2, y=4, intersection point (1/2,4)

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cos theta = 4/5, 0˚< theta < 90˚ use the information given to find sin2theta, cos2theta, and tan 2theta

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We take positive value of sinθ because 0° < θ < 90°
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$\sin2\theta=2\sin\theta\cos\theta=2\cdot\dfrac{3}{5}\cdot\dfrac{4}{5}=\dfrac{2\cdot3\cdot4}{5\cdot5}=\dfrac{24}{25}\\\\\\\cos2\theta=\cos^2\theta-\sin^2\theta=\left(\dfrac{4}{5}\right)^2-\left(\dfrac{3}{5}\right)^2=\dfrac{16}{25}-\dfrac{9}{25}=\dfrac{7}{25}\\\\\\
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