Solve the system of equations 3x = 84 - 2y 9x = 8y - 24

Mathematics

1 answer:

Eduardwww [97]2 years ago

8 0

Answer:

$3x = 84 - 2y - - - (i) \\ 9x = 8y - 24 - - - - (ii) \\ from \: (ii) \\ 3(3x) = 8y - 24 \\ but \: from \: (i) \: \: 3x = 84 - 2y \\ hence \: put \: (i) \: in \: (ii) \\ 3(84 - 2y) = 8y - 24 \\ 252 - 6y = 8y - 24 \\ 276 = 14y \\ y = \frac{138}{7} \\ x = \frac{104}{7}$

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DEF rotates 90 degrees clockwise about point A to create D’E’F. Therefore, which equation must be true

Rom4ik [11]

Answer:

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Step-by-step explanation:

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The LCM of two numbers is 60. Their GCf is 6 and their difference is 18. What are the two numbers?

Aliun [14]

$LCM(x,y)=60\\
GCF(x,y)=6\\
x-y=18\\\\
LCM(x,y)=\dfrac{|x\cdot y|}{GCD(x,y)}\\
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|x\cdot y|=360\\\\\\
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x=18+y\\\\
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(y+9)^2=441 \vee (y+9)^2=-279\\
y+9=\sqrt{441} \vee y+9=-\sqrt{441}\\
y=21-9 \vee y=-21-9\\
y=12 \vee y=-30\\\\
x-12=18 \vee x-(-30)=18\\
x=30 \vee x=-12\\\\
\boxed{x=30, y=12 \vee x=-12, y=-30}$