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2 years ago

\begin{aligned} & 2x+7y = 3 \\\\ & x=-4y \end{aligned}

Mathematics

1 answer:

zheka24 [161]2 years ago

4 0

Answer:

x = 12 , y = -3

Step-by-step explanation:

Solve the following system:

{2 x + 7 y = 3 | (equation 1)

x = -4 y | (equation 2)

Express the system in standard form:

{2 x + 7 y = 3 | (equation 1)

x + 4 y = 0 | (equation 2)

Subtract 1/2 × (equation 1) from equation 2:

{2 x + 7 y = 3 | (equation 1)

0 x+y/2 = -3/2 | (equation 2)

Multiply equation 2 by 2:

{2 x + 7 y = 3 | (equation 1)

0 x+y = -3 | (equation 2)

Subtract 7 × (equation 2) from equation 1:

{2 x+0 y = 24 | (equation 1)

0 x+y = -3 | (equation 2)

Divide equation 1 by 2:

{x+0 y = 12 | (equation 1)

0 x+y = -3 | (equation 2)

Collect results:

Answer: {x = 12 , y = -3

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3 years ago

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Alenkasestr [34]

Answer:

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Step-by-step explanation:

The sum of the measures of the angles of a triangle is 180 deg. Add the three measures and set equal to 180. Solve for x. then use the value of x and the expression for m<A to find the measure of angle A.

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2 years ago

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3 years ago

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2 years ago

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andreev551 [17]

Answer: $\bold{5)\ \cos \theta=\dfrac{\sqrt{11}}{6}\qquad 6)\ \tan \theta =\dfrac{8}{17}\qquad 7)\ \cos \theta = \dfrac{4}{3}\qquad 8)\ \cos \theta = \dfrac{\sqrt{10}}{10}}$

Step-by-Step Explanation:

Pythagorean Theorem is: a² + b² = c² , where "c" is the hypotenuse

$5)\ \cos \theta=\dfrac{\text{side adjacent to}\ \theta}{\text{hypotenuse of triangle}}=\dfrac{3\sqrt{11}}{18}\quad \rightarrow \large\boxed{\dfrac{\sqrt{11}}{6}}$

Note: (15)² + (3√11)² = hypotenuse² → hypotenuse = 18

$6)\ \cos \theta=\dfrac{\text{side adjacent to}\ \theta}{\text{hypotenuse of triangle}}=\dfrac{8}{17}\quad =\large\boxed{\dfrac{8}{17}}$

Note: 8² + 15² = hypotenuse² → hypotenuse = 17

$7)\ \tan \theta=\dfrac{\text{side opposite to}\ \theta}{\text{side adjacent to}\ \theta}=\dfrac{20}{15}\quad \rightarrow \large\boxed{\dfrac{4}{3}}$

Note: hypotenuse not needed for tan

$8)\ \cos \theta=\dfrac{\text{side adjacent to}\ \theta}{\text{hypotenuse of triangle}}=\dfrac{2}{2\sqrt{10}}\quad =\large\boxed{\dfrac{\sqrt{10}}{10}}$

Note: 2² + 6² = hypotenuse² → hypotenuse = 2√10

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2 years ago