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3 years ago

How many solutions does the system have? (x+2y=2 2x + 4y = -8

Mathematics

2 answers:

SIZIF [17.4K]3 years ago

6 0

Answer:

<h2>0 - no solution</h2>

Step-by-step explanation:

$\text{Let}\\\\\left\{\begin{array}{ccc}ax+by=c\\dx+ey=f\end{array}\right\\\\\text{in its simplest form, i.e. that a and b, d and e are relatively first}$

$\text{if}\ a=d,\ b=e,\ c=f,\ \text{then a system of equations has infinitely many solutions}\\\\\text{Example:}\\\\\left\{\begin{array}{ccc}x+3y=6\\-2x-6y=-12&\text{divide both sides by (-2)}\end{array}\right\\\\\left\{\begin{array}{ccc}x+3y=6\\x+3y=6\end{array}\right$

$\text{if}\ a=d,\ b=e,\ c\neqf,\ \text{then the system of equations has no solution}\\\\\text{Example:}\\\\\left\{\begin{array}{ccc}3x+9y=12&\text{divide both sides by 3}\\x+3y=1\end{array}\right\\\\\left\{\begin{array}{ccc}x+3y=4\\x+3y=1\end{array}\right$

$\text{In other cases it has one solution.}$

$\text{We have:}\\\\\left\{\begin{array}{ccc}x+2y=2\\2x+4y=-8&\text{divide both sides by 2}\end{array}\right\\\\\left\{\begin{array}{ccc}x+2y=2\\x+2y=-4\end{array}\right\\\\\text{Conclusion:}\\\\\text{The system of equations has no solution.}$

$\text{Now I will show it}$

$\left\{\begin{array}{ccc}x+2y=2\\x+2y=-8&\text{change the sings}\end{array}\right\\\underline{+\left\{\begin{array}{ccc}x+2y=2\\-x-2y=8\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad0=10\qquad\bold{FALSE}$

pogonyaev3 years ago

3 0

Answer:

Step-by-step explanation:

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How do you solve Ax+3y=48 for A?

olga_2 [115]

A=-3y/x+48/x
Hope this helps

3 0

3 years ago

A geologist visits 40 volcanoes in Alaska and California. 15% of the volcanoes are in California.

kotegsom [21]

Answer:

<h2>Most explained:</h2>

40% = 100%

15 = (100% - 15% = 85%) 85% in Alaska

California = 15% of 40 = (0.15 x 40) = 6

Alaska = 85% of 40 = (0.85 x 40) = 34

<h2>The simple way (or the way i found it simple):</h2>

<h3>(I found the simple way after i solve the first way)</h3>

Bye, i hope this helps.

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3 0

3 years ago

Simplify 10+6/2+3 pls help quickly

bixtya [17]

10+6=16
2+3=5
16/5 or 3.2
The answer is 16/5 or 3.2

6 0

3 years ago

What is the solution of the linear-quadratic system of equations? { y = x 2 + 5 x − 3 y − x = 2

svp [43]

The two solutions for the system of equations:

y = x^2+ 5x - 3

y - x = 2

Are:

(-5, -7) and (1, -1)

<h3>How to solve the system of equations?</h3>

Here we have the following system of equations:

y = x^2+ 5x - 3

y - x = 2

We can replace the first equation into the second one to get:

(x^2+ 5x - 3) - x = 2

x^2 + 4x - 3 = 2

x^2 + 4x - 3 - 2 = 0

x^2 + 4x - 5 = 0

Using the quadratic formula, we will get the solutions:

$x = \frac{-4 \pm \sqrt{4^2 - 4*1*-5} }{2} \\\\x = \frac{-4 \pm 6}{2}$

The two solutions are:

x = (-4 - 6)/2 = -5

x = (-4 + 6)/2 = 1

To find the values of y, we can evaluate the linear equation:

when x = -5

y - (-5) = -2

y + 5 = -2

y = -2 - 5 = -7

So one solution is (-5, -7)

when x = 1

y - 1 = -2

y = -2 + 1 = -1

The other solution is (1, -1)

Learn more about systems of equations:

brainly.com/question/13729904

#SPJ1

5 0

1 year ago

Apex Fitness Club uses straight-line depreciation for a machine costing $24,600, with an estimated four-year life and a $2,500 s

Brums [2.3K]

Answer:

machine's book value at the end of its second year = $13550

the amount of depreciation for each of the final three years = $3833.33

Step-by-step explanation:

machine costing $24,600

4 year salvage value = $2,500

3 year salvage value = $2,050

to find out

machine's book value at the end of its second year and the amount of depreciation for each of the final three years

solution

first w calculate depreciate basis = machine costing - 4 year salvage value

depreciate basis = $24600 - $2500 = $22100

and depreciate = $22100 / 4 = $5525 per year

so after 2 year depreciate value is 2 × $5525 = $11050

now we can say machine's book value at the end of its second year = machine costing - after 2 year depreciate value

machine's book value at the end of its second year = $24,600 - $11050

machine's book value at the end of its second year = $13550

and the amount of depreciation for each of the final three years = ( book value - salvage value ) / 3

the amount of depreciation for each of the final three years = ( $13550 - $2,050 ) / 3

the amount of depreciation for each of the final three years = $3833.33

8 0

3 years ago