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3 years ago

Solve this system of linear equations.separate the x- and y-value with a comma. -6x=-4-y -7x=-22+y.

Mathematics

2 answers:

scZoUnD [109]3 years ago

8 0

Answer:

(2,8)

Step-by-step explanation:

Add them together to get rid of the y.

-6x = -4 - y

-7x = -22 + y

-13x = -26

Then solve for x.

-13x/-13 = -26/-13

x = 2

Now plug in the x value into either equation and solve for y.

-7(2) = -22 + y

-14 = -22 + y

-14 + 22 = -22 + 22 + y

8 = y

So...

x = 2

y = 8

(2,8)

Eddi Din [679]3 years ago

6 0

Answer:

The solution is (-2, -16).

Step-by-step explanation:

-6x = -4-y can be solved for y: y = 6x - 4

-7x = -22 + y

In the second equation, substitute 6x - 4 for y:

-7x = -22 + 6x - 4

Grouping like terms: 0 = -22 + 6x + 7x - 4, or

-26 = 13x

So x = -2. If x = -2, we can obtain the value of y from y = 6x - 4 (see above).

y = 6(-2) - 4 = -16

The solution is (-2, -16).

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Please find the attached diagram for a better understanding of the question.

As we can see from the diagram,

RQ = 21 feet = height of the hill

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$\angle x=\angle RPQ$ = which is unknown.

Let us begin solving now. The first step is to find the angle $\angle x$ which can be found by using the following trigonometric ratio in $\Delta PQR$ :

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Which gives $\angle x$ to be:

$\angle x=tan^{-1}(\frac{21}{57})\approx20.22^{0}$

Now, we know that $\angle x$ and $\angle SPR$ can be added to give us the complete angle $\angle SPQ$ in the right triangle $\Delta SPQ$ .

We can again use the tan trigonometric ratio in $\Delta SPQ$ to solve for the height of the statue, h.

This can be done as:

$tan(\angle SPQ)=\frac{SQ}{PQ}$

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$tan(27.32^0)=\frac{h+21}{57}$

$\therefore h+21=57tan(27.32^0)$

$h\approx8.45 ft$

Thus, the height of the statue is approximately, 8.45 feet.

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