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Natalija [7]
2 years ago
15

NEED HALP!!! Find the ordered pair $(s,t)$ that satisfies the system

Mathematics
1 answer:
satela [25.4K]2 years ago
5 0

Answer:

(-8/7 ; 5/7)

Step-by-step explanation:

5t + 1/2s = 3 - - - (1)

3t - 6s = 9 - - - - - (2)

Multiply (1) by 12 and (2) by 1

Add the result to eliminate s

60t + 6s = 36

3t - 6s = 9

____________

63t = 45

t = 45 / 63

t = 5/7

Put t = 5/7 in either (1) or (2) to obtain the value of s

3(5/7) - 6s = 9

15/7 - 6s = 9

-6s = 9 - 15/7

-6s = (63 - 15)/7

-6s = 48/7

s = 48/7 * - 1/6

s = - 8/7

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Theresa Morgan a chemist has a 10% hydrochloric acid solution and a 65% hydrochloric acid solution. How many liters of each shou
prisoha [69]

<u>ANSWER: </u>

170 liters of 10% hydrochloric acid must be mixed with 1700 liters of 65% hydrochloric acid solution to obtain 1870 liters of 60% solution.

<u>SOLUTION: </u>

First, set up a table. Fill in the unknowns with variables x and y. The table is attached below

From this, we can easily set up the two equations.  

Sum of values of two acids = Value of mixture  

0.1x + 0.65y = 1122  

For convenience, we'll multiply the entire equation by 100,

10x + 65y = 112200   ------ (1)  

Now, Sum of amounts of each acid = Amount of mixture  

x + y = 1870  ---------(2)

multiply (2) with 10 for easy calculation and derive the equation into one variable.

10x + 10y = 18700  

Subtracting equation (2) from (1),  

( + ) 10x + 65y = 112200

( − ) 10x + 10y = 18700

we get the solution as,

0 + 55y = 93500

Thus, 55y = 93500

y = 1700

Substituting y = 1700 in (2),

x + 1700 = 1870  

x  = 1870 - 1700  

x  = 170  

So, we have x = 170 and y = 1700

We can conclude that 170 liters of 10% hydrochloric acid must be mixed with 1700 liters of 65% hydrochloric acid solution  to obtain 1870 liters of 60% solution.

4 0
3 years ago
2y-x=6 and y=2x+7 graphed equals how many solutions​
zhannawk [14.2K]

Answer:

One solution

<em>BRAINLIEST, PLEASE!</em>

Step-by-step explanation:

2y - x = 6

2y = x + 6

y = x/2 + 3

y = 2x + 7

After graphing, they have one solution at (-2.667, 1.667).

8 0
2 years ago
Iv)<br>6x+3y=6xy<br>2x + 4y= 5xy​
Margaret [11]

Answer:

Ok, we have a system of equations:

6*x + 3*y = 6*x*y

2*x + 4*y = 5*x*y

First, we want to isolate one of the variables,

As we have almost the same expression (x*y) in the right side of both equations, we can see the quotient between the two equations:

(6*x + 3*y)/(2*x + 4*y) = 6/5

now we isolate one off the variables:

6*x + 3*y = (6/5)*(2*x + 4*y) =  (12/5)*x + (24/5)*y

x*(6 - 12/5) = y*(24/5  - 3)

x = y*(24/5 - 3)/(6 - 12/5) = 0.5*y

Now we can replace it in the first equation:

6*x + 3*y = 6*x*y

6*(0.5*y) + 3*y = 6*(0.5*y)*y

3*y + 3*y = 3*y^2

3*y^2 - 6*y = 0

Now we can find the solutions of that quadratic equation as:

y = \frac{6 +- \sqrt{(-6)^2 - 4*3*0} }{2*3} = \frac{6 +- 6}{6}

So we have two solutions

y = 0

y = 2.

Suppose that we select the solution y = 0

Then, using one of the equations we can find the value of x:

2*x + 4*0 = 5*x*0

2*x = 0

x = 0

(0, 0) is a solution

if we select the other solution, y = 2.

2*x + 4*2 = 5*x*2

2*x + 8 = 10*x

8 = (10 - 2)*x = 8x

x = 1.

(1, 2) is other solution

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3 years ago
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