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2 years ago

PLEASE HELP!!! A system of linear equations is shown below.

Mathematics

1 answer:

MAXImum [283]2 years ago

5 0

Answer:

The value of the variable x is -2 and the value of the variable y is -7.

Step-by-step explanation:

The substitution method consists of:

Solve for an unknown in one of the equations, which will be a function of the other unknown .
In the other equation that is not used, the same unknown is replaced by the expression obtained in step 1.
Solve for the only remaining unknown, obtaining the numerical value of an unknown.
Substitute the cleared unknown in step 3 for its numerical value in the equation obtained in step 1.
Operate to obtain the numerical value of the other unknown.

In this case, you have the system of equations:

$\left \{ {{2*x-3*y=17} \atop {-3*x+y=-1}} \right.$

Isolating the variable y from the second equation:

y= -1 +3*x

Replacing this expression in the first equation:

2*x-3*( -1 +3*x)= 17

Solving:

2*x -3*(-1)-3*3*x= 17

2*x +3 -9*x= 17

2*x -9*x= 17 -3

(-7)*x= 14

x= 14÷(-7)

x= -2

Now, replacing the value of x in the expression y = -1 + 3 * x you get:

y= -1 +3*(-2)

Solving:

y= -1 -6

y= -7

So, the value of the variable x is -2 and the value of the variable y is -7.

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Answer:

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Here are the steps:

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3 years ago

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nydimaria [60]

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3 years ago

GARY DREW A RECTANGLE WITH A PERIMETER OF 20 INCHES. WHAT COULD BE THE LENGTH,WIDTH,AND AREA FOR THE RECTANGLE THAT GARY DREW?

Ilia_Sergeevich [38]

Assume L=1.5W, where W=width, L= Length of the triangle.

Therefore,

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3 years ago

I need help with #8. I need to use the quadratic formula. I have a calculator that is programmed for the quadratic formula so al

GuDViN [60]

Answer:

x = 14

Step-by-step explanation:

Extend line AB so that it intersects ray CE at point G. Then angles BGC and BAD are "alternate interior angles", hence congruent.

The angle at B is exterior to triangle BCG, and is equal to the sum of the interior angles at C and G:

138 = (376 -23x) +(x^2 -8x)

Subtracting 138 and collecting terms we have ...

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Additional comment

You will find that the solutions to this are x = {14, 17}. You will also find that angle BCE will have corresponding values of 54° and -15°. That is, the solution x=17 is "extraneous." It is a solution to the equation, but not to the problem.

For x=14, the marked angles are A = 84°, C = 54°.

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3 years ago

part 2. Find the value of the trig function indicated, use for that Pythagorean theorem to find the third side if you need it.

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