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3 years ago

Which of these statements is correct?

Mathematics

2 answers:

tatuchka [14]3 years ago

8 0

Answer:

The system of linear equations 8x - 3y = 10 and 16x - 6y = 22 has no solution is correct.

Step-by-step explanation:

1) The system of linear equations 6x - 5y = 8 and 12x - 10y = 16 has no solution.

Solve these linear equations simultaneously

Step 1 : Find y in terms of x from any one equation

6x - 5y = 8

y = 8 - 6x

-5

Step 2 : Substitute y in terms of x from step 1 in the second equation.

16x - 6y = 22

16x - 6 (8 - 6x) = 22

-5

80x - 48 + 36x = 22 x -5

94x = 43

x = 0.457

This statement is incorrect as it does have a solution.

2) The system of linear equations 7x + 2y = 6 and 14x + 4y = 16 has an infinite number of solutions.

Solve these linear equations simultaneously

Step 1 : Find y in terms of x from any one equation

7x + 2y = 6

y = 6 - 7x

Step 2 : Substitute y in terms of x from step 1 in the second equation.

14x + 4y = 16

14x + 4(6 - 7x) = 16

14x + 12 - 14x = 16

0 ≠ 4

This statement is not true as there are no solutions.

3) The system of linear equations 8x - 3y = 10 and 16x - 6y = 22 has no solution.

Solve these linear equations simultaneously

Step 1 : Find x in terms of y from any one equation

8x - 3y = 10

x = 10 + 3y

Step 2 : Substitute x in terms of y from step 1 in the second equation.

16x - 6y = 22

16(10 + 3y) - 6y = 22

20 + 6y - 6y = 2

0 ≠ -18

This statement is true because there are no solutions

4) The system of linear equations 9x + 6y = 14 and 18x + 12y = 26 has an infinite number of solutions.

Solve these linear equations simultaneously

Step 1 : Find x in terms of y from any one equation

9x + 6y = 14

x = 14 - 6y

Step 2 : Substitute x in terms of y from step 1 in the second equation.

18x + 12y = 26

18 (14 - 6y) + 12y = 26

8 - 12y + 12y = 26

0 ≠ 18

This statement is incorrect because there are no solutions. It does not have infinite number of solutions.

!!

klasskru [66]3 years ago

8 0

Answer:

<h2>The system of linear equations 8x - 3y = 10 and 16x - 6y = 22 has no solution.</h2>

Step-by-step explanation:

The true statement is the third one, because that system of equations has no solutions. This is because those lines are parallel, see image attached.

We can demonstrate this by solving the system:

$\left \{ {{8x-3y=10} \atop {16x-6y=22}} \right.$

If we multiply the first equation by -2, we would have

$\left \{ {{-16x+6y=-20} \atop {16x-6y=22}} \right\\0x+0y=2\\0=2$

When this happens, means that the system has no solution, that is, the lines that represents those linear equations, are parallel.

Therefore, the right answer is the third option.

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3 years ago

Read 2 more answers

Which description best represents the inequality: 8x < x + 6?

Ugo [173]

Answer:

x < 6/7

Step-by-step explanation:

Your question doesn't say what your choices are, so I'm assuming the inequality should be solved for x... which values of x make 8x < x + 6?

Subtract x from both sides, then divide by 7.

7x < 6

x < 6/7

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3 years ago

I need help with numbers 7,8

meriva

Answer:

7.) the angle is an acute

8.) the angle is an obtuse

Step-by-step explanation:

an acute is an angle lower than 90°

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3 years ago

PLEASE TELL ME!!!!!! What is the solution to the equation 4/5n-1/5=2/5n

Mashutka [201]

Answer:

4/5n-1/5=2/5n

One solution was found :

n = 1/2 = 0.500

Step-by-step explanation:

Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

4/5*n-1/5-(2/5*n)=0

Step by step solution :

Step 1 :

Simplify —

Equation at the end of step 1 :

4 1 2

((—•n)-—)-(—•n) = 0

5 5 5

Step 2 :

Simplify —

Equation at the end of step 2 :

4 1 2n

((— • n) - —) - —— = 0

5 5 5

Step 3 :

Simplify —

Equation at the end of step 3 :

4 1 2n

((— • n) - —) - —— = 0

5 5 5

Step 4 :

Adding fractions which have a common denominator :

4.1 Adding fractions which have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

4n - (1) 4n - 1

———————— = ——————

5 5

Equation at the end of step 4 :

(4n - 1) 2n

———————— - —— = 0

5 5

Step 5 :

Adding fractions which have a common denominator :

5.1 Adding fractions which have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

(4n-1) - (2n) 2n - 1

————————————— = ——————

5 5

Equation at the end of step 5 :

2n - 1

—————— = 0

Step 6 :

When a fraction equals zero :

6.1 When a fraction equals zero ...

Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.

Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.

Here's how:

2n-1

———— • 5 = 0 • 5

Now, on the left hand side, the 5 cancels out the denominator, while, on the right hand side, zero times anything is still zero.

The equation now takes the shape :

2n-1 = 0

Solving a Single Variable Equation :

6.2 Solve : 2n-1 = 0

Add 1 to both sides of the equation :

2n = 1

Divide both sides of the equation by 2:

n = 1/2 = 0.500

One solution was found :

n = 1/2 = 0.500

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4 years ago

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Anni [7]

Answer:

At what type of boundary do strike-strip basins form? transform

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Step-by-step explanation:

Hope this helps!

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4 years ago