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3 years ago

What is the solution set for the following system of equations 5x-3y-10=0 x+y-7=0

Mathematics

1 answer:

garik1379 [7]3 years ago

6 0

(x, y) = ( $\frac{31}{8}$ , $\frac{25}{8}$ )

given the 2 equations

5x - 3y - 10 = 0 → (1)

x + y - 7 = 0 → (2)

rearrange (2) to obtain y in terms of x

y = 7 - x → (3)

Substitute y = 7 - x into (1)

5x - 3(7 - x) - 10 = 0

5x - 21 + 3x - 10 = 0

8x - 31 = 0 ( add 31 to both sides )

8x = 31 ( divide both sides by 8 )

x = $\frac{31}{8}$

Substitute this value into (3) for y

y = 7 - x = $\frac{56}{8}$ - $\frac{31}{8}$ = $\frac{25}{8}$

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Please help quickly thanks :)

marusya05 [52]

(0, 0) → t = 0, w = 0 → w = 0 · 0

(1, 4) → t = 1, w = 4 → w = 1 · 4

(2, 8) → t = 2, w = 8 → w = 2 · 4

(3, 12) → t = 3, w = 12 → w = 3 · 4

<h3>Answer: w = 4t</h3>

8 0

2 years ago

A home gardener estimates that 18 apple trees will produce an average yield of 80 apples per tree. But because of the size of th

aliina [53]

19 trees should be planted to maximize the total

<h3>How many trees should be planted to maximize the total</h3>

From the question, we have the following parameters:

Number of apples, x = 18

Yield, f(x) = 80 per tree

When the number of apple trees is increased (say by x).

We have:

Trees = 18 + x

The yield decreases by four apples per tree.

So, we have

Yield = 80 - 4x

So, the profit function is

P(x) = Apples * Yield

This gives

P(x) = (18 + x) *(80 - 4x)

Expand the bracket

P(x) = 1440 - 72x + 80x - 4x^2

Differentiate the function

P'(x) = 0 - 72 + 80 - 8x

Evaluate the like terms

P'(x) = 8 - 8x

Set P'(x) to 0

8 - 8x = 0

Divide through by 8

1 - x = 0

Solve for x

x = 1

Recall that:

Trees = 18 + x

So, we have

Trees = 18 + 1

Evaluate

Trees = 19

Hence, 19 trees should be planted to maximize the total

Read more about quadratic functions at:

brainly.com/question/12120831

#SPJ1

4 0

1 year ago

Help with this work pls

Travka [436]

Answer:

(6, 2), (0, -2), (-3, -4)

Step-by-step explanation:

The intercepts are clearly (0, -2) and (3, 0). This eliminates the bottom two choices.

Both of these are listed in the upper left choice, but the third point there, (-6, -5), is not on the graph. This leaves only the upper right choice. Checking the remaining two points in that choice, (6, 2) and (-3, -4), confirms they are both on the graph.

8 0

2 years ago

Diona told me to get this app to solve my math problems,what is 10 + 10 Jean can't help because she's doing other stuff :,)

elena55 [62]

Answer:

Step-by-step explanation:

10 + 10

= 20

Just add units place first.

0 + 0 = 0

Then tens place.

1 + 1 = 2

So the number,

=> 20

5 0

2 years ago

James has a bag 77 of nickels and dimes. The total value of coins is $6.60. How many dimes does James have?

tatuchka [14]

James has 55 dimes in the bag

Step-by-step explanation:

The given is:

James has in a bag 77 of nickels and dimes
The total value of coins is $6.60

We need to find how many dimes James has

Assume that the number of nickels is x and the number of

dimes is y in the bag

∵ There are x nickels in the bag

∵ There are y dimes in the bag

∵ There are 77 coins in the bag

∴ x + y = 77 ⇒ (1)

∵ 1 nickel = 5 cents

∴ The value of nickles in the bag = 5x cents

∵ 1 dime = 10 cents

∴ The value of dimes in the bag = 10y cents

∵ The total value of coins is $6.60

∵ 1 dollar = 100 cents

∴ $6.60 = 6.60 × 100 = 660 cents

∴ 5x + 10y = 660 ⇒ (2)

Now we have a system of equations to solve it

Multiply equation (1) by -10 to eliminate y

∵ -10x - 10y = -770 ⇒ (3)

- Add equations (2) and (3)

∴ -5x = -110

- Divide both sides by -5

∴ x = 22

Substitute the value of x in equation (2) to find y

∵ 22 + y = 77

- Subtract 22 from both sides

∴ y = 55

∴ The number of dimes is 55

James has 55 dimes in the bag

Learn more:

You can learn more about the system of equations in brainly.com/question/6075514

#LearnwithBrainly

6 0

3 years ago