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3 years ago

Solve the system using elimination: -5x + 3y = 2 for x -5x - 5y = -30 for y

Mathematics

1 answer:

LiRa [457]3 years ago

3 0

Hey there! :)

Equation 1 : -5x + 3y = 2

Equation 2 : -5x - 5y = -30

Because both equations contain a like term (which in this case is 5x), we can easily subtract these equations from one another.

Subtract equation 1 from equation 2 :

-5x - (-5x) = 0

3y - (-5y) = 3y + 5y --> 8y

2 - (-30) = 2 + 30 --> 32

This leaves us with 8y = 32. Simplify this to get y by dividing both sides by 8.

8y ÷ 8 = 32 ÷ 8

Simplify.

y = 4

Now, plug in 4 for y in our first equation.

-5x + 3(4) = 2

Simplify.

-5x + 12 = 2

Subtract 12 from both sides.

-5x = 2 - 12

Simplify.

-5x = -10

Divide both sides by -5.

-5x ÷ -5 = -10 ÷ -5

Simplify.

x = 2

Therefore, our answer is :

(2, 4) where x = 2, y = 4

~Hope I helped!~

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How do I solve this problem ?

Nonamiya [84]

Answer:

$19.99 for each cartridge.

Step-by-step explanation:

For this problem, we are finding the cost of the three printer cartridges. Since the problem says that the tax was 5.95, we can subtract that from 90.91.

90.91-5.95=

84.96

Next, since we know that the software package was 24.99, we can subtract that from 84.96.

84.96-24.99=

59.97

Finally, since there are three printer cartridges, we can divide 59.97 by 3, and get our answer.

59.97/3=

19.99

Each printer cartridge would cost $19.99.

Hope this helps and have a good day! :D

8 0

1 year ago

LORAN is a long range hyperbolic navigation system. Suppose two LORAN transmitters are located at the coordinates (−60,0) and (6

USPshnik [31]

LORAN follows an hyperbolic path.

The equation of the hyperbola is: $\mathbf{\frac{x^2}{2500} + \frac{y^2}{1100} = 1}$

The coordinates are given as:

$\mathbf{(x,y) = (-60,0)\ (60,0)}$

The center of the hyperbola is

$\mathbf{(h,k) = (0,0)}$

The distance from the center to the focal points is given as:

$\mathbf{c = 60}$

Square both sides

$\mathbf{c^2 = 3600}$

The distance from the receiver to the transmitters is given as:

$\mathbf{2a = 100}$

Divide both sides by 2

$\mathbf{a = 50}$

Square both sides

$\mathbf{a^2 = 2500}$

We have:

$\mathbf{b^2 = c^2 - a^2}$

This gives

$\mathbf{b^2 = 3600 - 2500}$

$\mathbf{b^2 = 1100}$

The equation of an hyperbola is:

$\mathbf{\frac{(x - h)^2}{a^2} + \frac{(y - k)^2}{b^2} = 1}$

So, we have:

$\mathbf{\frac{(x - 0)^2}{2500} + \frac{(y - 0)^2}{1100} = 1}$

$\mathbf{\frac{x^2}{2500} + \frac{y^2}{1100} = 1}$

Hence, the equation of the hyperbola is: $\mathbf{\frac{x^2}{2500} + \frac{y^2}{1100} = 1}$

Read more about hyperbolas at:

brainly.com/question/15697124

7 0

3 years ago

Read 2 more answers

If x > 0 and y > 0, where is the point (x, y) located?

Scrat [10]

Given, x > 0, y > 0.
So, the values of x and y are less than 0, that means, they are negative integers.
If we divide a Cartesian plane with the x-axis and y-axis, we get four quadrants.
1st Quadrant : (+,+)
2nd Quadrant : (-,+)
3rd Quadrant : (-,-)
4th Quadrant : (+,-)
Since the values of x and y are both negative, so (x, y) is located in the 3rd Quadrant.

Hope you could get an idea from here.

Doubt clarification - use comment section

8 0

2 years ago

PLEASE HELP!!!

Blababa [14]

Answer:

x = 12, y = 17

Step-by-step explanation:

x+5 = 2x-7

x = 12

y = x+5 = 17