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jekas [21]
3 years ago
11

Use the substitution and to rewrite the equations in the system in terms of the variables and . Solve the system in terms of u a

nd v . Then back substitute to determine the solution set to the original system in terms of x and y.
-3/x+4/y=11
1/x-2/y=-5
Mathematics
1 answer:
Tatiana [17]3 years ago
4 0

Answer:

x = -1 and y = 1/2

Step-by-step explanation:

Let u = 1/x, and v = 1/y

Then the pair of equations

-3/x + 4/y = 11

1/x - 2/y = -5

Can be written as

-3u + 4v = 11 .................................(1)

u - 2v = -5......................................(2)

From (2)

u = 2v - 5 .......................................(3)

Substituting (3) into (1)

-3(2v - 5) + 4v = 11

-6v + 15 + 4v = 11

-6v + 4v = 11 - 15

-2v = -4

v = 4/2 = 2

Substituting this value of v in (3)

u = 2v - 5

u = 2(2) - 5

= 4 - 5

= -1

That is

u = -1, v = 2

Since u = 1/x, and v = 1/y, we have

1/x = -1

=> x = -1

And

1/y = 2

=> y = 1/2

Therefore

x = -1 and y = 1/2

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A heart will beat 140 times in 2 minutes

Step-by-step explanation:

700 ÷ 10 = 70

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5 0
3 years ago
1 and 16/24 + 1 and 21/24
AlexFokin [52]

Answer:

turn into improper fractions

1*24+16=40

40/24

1*24+21=45

45/24

40/24+45/24=85/24

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6 0
3 years ago
A student drives 4.8-km trip to school and averages a speed of 22.6 m/s. on the return trip home, the student travels with an av
ArbitrLikvidat [17]

In this case, we cannot simply take the average speed by adding the two speeds and divide by two.

What we have to do is to calculate the time required going to school and the return trip home.

We know that to calculate time, we use the formula:

t = d / v

where,

d = distance = 4.8 km = 4800 m

v = velocity

 

Let us say that the variables related to the trip going to school is associated with 1, and the return trip home is 2. So,

 

t1 = 4800 m / (22.6 m / s)

t1 = 212.39 s

 

t2 = 4800 / (16.8 m / s)

t2 = 285.71 s

 

total time, t = t1 + t2

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Therefore the total average velocity is:

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Answer:

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4 0
3 years ago
Read 2 more answers
If PQR ~ UTV, find the value of x.
user100 [1]

The value of x is 15.

Solution:

Given ΔPQR \sim ΔUTV.

<em>If two triangles are similar, then the corresponding parts are congruent.</em>

$\Rightarrow \frac{PR}{UV} =\frac{RQ}{VT}

$\Rightarrow \frac{14}{x + 6} =\frac{8}{x -3}

Do cross multiplication, we get

⇒ 14(x - 3) = 8(x + 6)

⇒ 14x - 42 = 8x + 48

Add 42 on both sides.

⇒ 14x = 8x + 90

Subtract 8x on both sides.

⇒ 6x = 90

Divide by 6 on both sides.

⇒ x = 15

The value of x is 15.

5 0
3 years ago
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