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barxatty [35]
3 years ago
12

Find the solution of the system of equations. 15x – 4y = -50 3x – 2y = –16

Mathematics
1 answer:
rusak2 [61]3 years ago
7 0

Answer:

x=-2, y=5. (-2, 5).

Step-by-step explanation:

15x-4y=-50

3x-2y=-16

---------------

15x-4y=-50

-5(3x-2y)=-5(-16)

------------------------

15x-4y=-50

-15x+10y=80

-------------------

6y=30

y=30/6

y=5

3x-2(5)=-16

3x-10=-16

3x=-16+10

3x=-6

x=-6/3

x=-2

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Using the Extended Euclidean Algorithm, find integers x and y such that 26x + 9y = 1.
Xelga [282]

Answer:

The solution is: x=-1 and y=3.

Step-by-step explanation:

Let's find the solution, but first let's remember the following:

A / B = C + R where:

A=dividend, B=divisor, C=quotient, and R=remainder. This can be express as follows:

A = (C * B) + R, which is the structure we are going to use next.

Using the Euclidian Algorithm we need to find the highst common factor (HCF) between the coefficients from your equation, this means:

The original equation: 26x+9y=1 is in the form Ax+By=C, so A=26, B=9 and C=1.

We need to find the HCF of 'A' and 'B'. Using the Euclidan Algorithm (EA), so we have:

A = (C * B) + R, using our values:

26 = (2 * 9) + 8, look that the divisor (B) is 9 and the remainder (R) is 8.

Now using the (EA) we divide the divisor (B=9) by the obtained remainder (R=8). And we do the same for each obtained result until the las remainder (R) is equal to 0, like this:

A = (C * B) + R

9 = (8 * 1) + 1

using the divisor (B=8) and the remainder (R=1) we obtain:

A = (C * B) + R

8 = (1 * 8) + 0, look that the remainder is now 0, so in summary we can use the method as follows:

26 = (2 * 9) + 8

9 = (8 * 1) + 1

8 = (1 * 8) + 0; and this equations are the ones we are going to use in order to find a solution.

Next step is to use the equation before R=0, so:

9 = (8 * 1) + 1, which is:

9 - (8 * 1) = 1; but if you consider the first obtained equation: 26 = (2 * 9) + 8, we can write:

26 - (2 * 9) = 8, and we can use this expression in the previous one, so:

9 - (8 * 1) = 1, is:

9 - ((26 - (2 * 9)) * 1) = 1, simplifying:

9 - 26 + (2*9) = 1

9 - 26 + (9 + 9) = 1

-26 + (9 + 9 + 9) = 1

-26 + (3 * 9) = 1

26*(-1) + 9*(3) = 1; if you compare the last expression with the original equation, which is: 26x+9y=1, you can see the similarity, where x=-1 and y=3.

So, the solution is: x=-1 and y=3.

8 0
3 years ago
A number line has marks A question mark, negative 2, B question mark, 0, 1, C-2, 3, D question mark, 5, E 6.
slavikrds [6]

Answer:

What number is represented by point B = -1  

Which point represents the number 2? = C

3 0
3 years ago
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Whitch is the value of this expression when a=5 and k=-2
lana66690 [7]

Answer:

25/9

Step-by-step explanation:

25/9

7 0
3 years ago
Can someone help me find x.
Harman [31]

Answer:

Step-by-step explanation:

6x+9=63

6x=63-9

6x=54

x=54/6

x=9

I encourage you to figure out the justification yourself.

8 0
3 years ago
Hi!
Dima020 [189]

Answer:

90 men

Step-by-step explanation:

just keep the ratio constant

3:7

equals 10 parts

300/10=30

3*30:7*30

90 men and 210 women

hope this helps!!! :)

5 0
3 years ago
Read 2 more answers
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