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3 years ago

What is the y-coordinate of the solution of the system? {3x+10y=7, x-10y=29}

1 answer:

8 0

We know that:

3x + 10y = 7

We also know that:

x - 10y = 29

Which means that:

x = 29 + 10y

If, x = 29 + 10y,

3(29 + 10y) + 10y = 7

3*29 + 30y + 10y = 7

3(20+9) + 40y = 7

60 + 27 + 40y = 7

87 + 40y = 7

40y = 7 - 87

40y= -80

y=(-80)/40

y=-2

Answer y=-2.

If y=-2,

x-10(-2)=29

x+20=29

x=29-20

x=9

Let's see if these results are true:

3(9)+10(-2)=7

27-20=7 (Correct)

-----------

9-10(-2)=29

9+20=29 (Correct)

Answer once again:

y=-2

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Dennis_Churaev [7]

Answer:

Step-by-step explanation:

If you want to find the equation of line with a given a slope of which goes through the point (-4,5), you can simply use the point-slope formula to find the equation:

---Point-Slope Formula---

where is the slope, and is the given point

So lets use the Point-Slope Formula to find the equation of the line

Plug in , , and (these values are given)

Distribute

Multiply and to get

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Combine like terms and to get the answer

So the equation of the line with a slope of which goes through the point (-4,5) is:

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2 years ago

Find thhe remainder when 7^203 is divided by 4

Aleksandr [31]

Using the square-and-multiply approach, we have

$7^{203}=7\times(7^{101})^2$
$7^{101}=7\times(7^{50})^2$
$7^{50}=(7^{25})^2$
$7^{25}=7\times(7^{12})^2$
$7^{12}=(7^6)^2$
$7^6=(7^3)^2$
$7^3=7\times7^2$

and so, using the property that, if $a_1\equiv b_1\mod n$ and $a_2\equiv b_2\mod n$ , then $a_1a_2\equiv b_1b_2\mod n$ , we get

$7\equiv3\mod4$
$7^2\equiv9\equiv1\mod4$
$7^3\equiv7\times1\equiv7\equiv3\mod4$
$7^6\equiv9\equiv1\mod4$
$7^{12}\equiv1\mod4$
$7^{25}\equiv7\times1\equiv7\equiv3\mod4$
$7^{50}\equiv9\equiv1\mod4$
$7^{101}\equiv7\times1\equiv7\equiv3\mod4$
$7^{203}\equiv7\times9\equiv3\times1\equiv3\mod4$

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I am Lyosha [343]

Answer:

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Dmitry_Shevchenko [17]

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