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otez555 [7]
3 years ago
10

5x + 3y = 16 3x -5y = -4 How do I solve this

Mathematics
1 answer:
lawyer [7]3 years ago
6 0

Answer:

(2, 2)

Step-by-step explanation:

We can solve this system of equations using the elimination method.

Let's start by multiplying the first equation by 3:

3(5x+3y)=3(16)\\3(5x)+3(3y)=48\\15x+9y=48

Now, multiply the second equation by 5:

5(3x-5y)=5(-4)\\5(3x)-5(5y)=-20\\15x-25y=-20

Since both equations have 15x, we can eliminate the x by subtracting the two equations.

15x-15x+9y-(-25y)=48-(-20)\\9y+25y=68\\34y=68\\\text{Divide both sides by 34}\\y=2

Now, substitute 2 for y to solve for x:

5x+3y=16\\5x+3(2)=16\\5x+6=16\\\text{Subtract 6 from both sides}\\5x=10\\\text{Divide both sides by 2}\\x=2

Therefore the solution to this system of equations is:

(x, y)=(2, 2)

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3 years ago
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Karl’s and eddie’s ages added together are equal to 65. 10 years ago, Karl was twice as old as Eddie. How old are they now
trapecia [35]

9514 1404 393

Answer:

  • Karl is 40
  • Eddie is 25

Step-by-step explanation:

10 years ago, the sum of their ages was 65 -2·10 = 45.

If Karl was twice as old as Eddie, his contribution was 2/3 of the sum and Eddie's was 1/3. That is, Karl was (2/3)(45) = 30 and Eddie was 15 at that time.

Now, Karl is 40 and Eddie is 25.

__

This can be solved using a system of equations.

  e = 65 -k

  (k -10) = 2(e -10)

Substituting the first equation into the second gives ...

  k -10 = 2((65 -k) -10)

  k -10 = 110 -2k . . . . . . . simplify

  3k = 120 . . . . . . . . . . . . add 10+2k

  k = 40

  e = 65 -40 = 25

7 0
3 years ago
What are the first five partial sums of the arithmetic sequence an = 0.05(n – 1) – 0.6?
Gnoma [55]
The sum of the arithmetic sequence given by
<span>an = 0.05(n – 1) – 0.6
will be given by:
a1=0.05(1-1)-0.6=-0.6
a2=0.05(2-1)-0.6=-0.55
a3=0.05(3-1)-0.6=-0.5
a4=0.05(4-1)-0.6=-0.45
a5=0.05(5-1)-0.6=-0.4
thus the summation will be:
-0.6+(-0.55)+(-0.5)+(-0.45)+(-0.4)
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S5=-2.5</span>
5 0
4 years ago
The sum of two numbers is −21. One number is 55 less than the other. Find the numbers.
nika2105 [10]

Answer:

x = 17     y= -38

Step-by-step explanation:

x + y = -21

y = x - 55

It doesn't matter whether x or y is 55 less than the other right now.

<u>substitute for y:</u>

x + x - 55 = -21

<u>solve for x:</u>

2x = 34

x = 17

<u>solve for y:</u>

17 + y = -21

y = -38

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