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3 years ago

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Solve the system of equations. 2.5y + 3x = 27 5x – 2.5y = 5 What equation is the result of adding the two equations? –8x = 328x

= 325y + 8x = 328x – 5y = 32 What is the solution to the system? (–4, 6)(–2.75, 8.6)(2.75, 3.5)(4, 6)

2 answers:

galben [10]3 years ago

4 0

A) The result of adding the two equations is
.. (2.5y +3x) +(5x -2.5y) = (27) +(5)
.. 8x = 32 . . . . . . . . . . . . . . . . . . . . . . . your 2nd selection

b) The solution to the system is (4, 6), your 4th selection.
.. This is the only choice with x=4, the solution to part (a).

nikitadnepr [17]3 years ago

3 0

Answer:

8x=32

(4,6)

Step-by-step explanation:

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Statements can be proved by contrapositive, contradiction or by induction.

<em>2.21 and 2.23 are proved by contrapositive</em>
<em>2.22 is proved by induction</em>

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<u>2.21: If </u> $n^3$ <u> is even, then n is even (By contrapositive)</u>

The contrapositive of the above statement is that:

<em>If n is odd, then </em> $n^3$ <em> is odd</em>

Represent the value of n as:

$n = 2k + 1$ , where $k \ge 0$

Take the cube of both sides

$n^3 = (2k + 1)^3$

Expand

$n^3 = 8k^3 + 6k^2 + 6k + 1$

Group

$n^3 =[ 8k^3 + 6k^2 + 6k] + 1$

Factor out 2

$n^3 =2[4k^3 + 3k^2 + 3k] + 1$

Assume w is an integer; where:

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So, we have:

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The constant term (i.e. 1) means that $n^3$ is odd.

Hence, the statement has been proved by contrapositive.

<em>i.e. If n is odd, then </em> $n^3$ <em> is odd</em>

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<u>2.22 </u> $3n + 4$ <u> is even, if and only if n is even</u>

We have: $3n + 4$ <u />

<u />

Assume that: $n = 2k + 2$ for $k \ge 0$

So, we have:

$3n + 4 = 3(2k + 2) + 4$

Open bracket

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Factorize

$3n + 4 = 2(3k + 5)$

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<u />

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The contrapositive of the above statement is:

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