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seropon [69]
2 years ago
12

PLEASE HELPPP!! Solve the system of equations.

Mathematics
1 answer:
sdas [7]2 years ago
5 0

Answer:

<u>x= 4 </u>

<u>y= -2</u>

<em>Step-by-step explanation:</em>

-3y+5x=26\\-2y-5x=-16

Solve by using the <u>Elimination Method.</u>

-5y=10\\\\\frac{-5y}{-5} =\frac{10}{-5} \\\\y=-2

Now plug y into one of the original equation.

=======================================

-2y-5x=-16

(-2*-2)-5x=-16

4-5x=-16

4-5x+5x=-16+5x

4+16=-16+5x+16

20=5x\\\\\frac{20}{5} =\frac{5x}{5} \\\\x=4

=======================================

\left \{ {{x=4} \atop {y=-2}} \right.

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Determine the truth value of each of these statements if thedomainofeachvariableconsistsofallrealnumbers.
hoa [83]

Answer:

a)TRUE

b)FALSE

c)TRUE

d)FALSE

e)TRUE

f)TRUE

g)TRUE

h)FALSE

i)FALSE

j)TRUE

Step-by-step explanation:

a) For every x there is y such that  x^2=y:

 TRUE

This statement is true, because for every real number there is a square         number of that number, and that square number is also a real number. For example, if we take 6.5, there is a square of that number and it equals 39.0625.

b) For every x there is y such that  x=y^2:

 FALSE

For example, if x = -1, there is no such real number so that its square equals -1.

c) There is x for every y such that xy = 0

 TRUE

If we put x = 0, then for every y it will be xy=0*y=0

d)There are x and y such that x+y\neq y+x

 FALSE

There are no such numbers. If we rewrite the equation we obtain an incorrect statement:

                                   x+y \neq y+x\\x+y - y-y\neq 0\\0\neq 0

e)For every x, if   x \neq 0  there is y such that xy=1:

 TRUE

The statement is true. If we have a number x, then multiplying x with 1/x (Since x is not equal to 0 we can do this for ever real number) gives 1 as a result.

f)There is x for every y such that if y\neq 0 then xy=1.

TRUE

The statement is equivalent to the statement in e)

g)For every x there is y such that x+y = 1

TRUE

The statement says that for every real number x there is a real number y such that x+y = 1, i.e. y = 1-x

So, the statement says that for every real umber there is a real number that is equal to 1-that number

h) There are x and y such that

                                  x+2y = 2\\2x+4y = 5

We have to solve this system of equations.

From the first equation it yields x=2-2y and inserting that into the second equation we have:

                                   2(2-2y)+4y=5\\4-4y+4y=5\\4=5

Which is obviously false statement, so there are no such x and y that satisfy the equations.

FALSE

i)For every x there is y such that

                                     x+y=2\\2x-y=1

We have to solve this system of equations.

From the first equation it yields x=2-y  and inserting that into the second equation we obtain:

                                        2(2-y)-y=1\\4-2y-y=1\\4-3y=1\\-3y=1-4\\-3y=-3\\y=1

Inserting that back to the first equation we obtain

                                            x=2-1\\x=1

So, there is an unique solution to this equations:

x=1 and y=1

The statement is FALSE, because only for x=1 (and not for every x) exists y (y=1) such that

                                         x+y=2\\2x-y=1

j)For every x and y there is a z such that

                                      z=\frac{x+y}{2}

TRUE

The statament is true for all real numbers, we can always find such z. z is a number that is halway from x and from y.

5 0
3 years ago
DJ wants to install a zipline between two trees. The zipline will be strung
jolli1 [7]

Answer:

104 ft total

Step-by-step explanation:

52 times 2 equals 104

8 0
3 years ago
What are the solutions of the quadratic equation (x + 3)2 = 49
Korvikt [17]

the right answer is

x = 4 and x = –10

I just take the test and I got it right I hope yall get it right to


8 0
3 years ago
Read 2 more answers
Which of the following best describes the solution to the system of equations below?
OverLord2011 [107]

Answer: OPTION A

Step-by-step explanation:

The equation of the line in slope-intercept form is:

y=mx+b

Where m is the slope and b the y-intercept.

Solve for y from each equation:

\left \{ {{5y=-4x+7} \atop {10y=-8x+14}} \right.\\\\\left \{ {{y=\frac{-4}{5}x+\frac{7}{5}} \atop {y=\frac{-8}{10}x+\frac{14}{10}}} \right.\\\\\left \{ {{y=\frac{-4}{5}x+\frac{7}{5}} \atop {y=\frac{-4}{5}x+\frac{7}{5}}} \right.

As you can see the slope and the y-intercept of each equation are equal, this means that both are the exact same line. Therefore, you can conclude that the system has infinitely many solutions.

3 0
3 years ago
How many times can 535 go into 1035
ICE Princess25 [194]
Only once, any number higher will pass it
3 0
3 years ago
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