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4 years ago

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If you were solving a system of equations and you came to a statement like 4 = 4, what do you know about the solution to the sys

tem? (1 point) The solution is (4, 4) The solution is x = 4 and y = 4 There is no solution There are infinitely many solutions

2 answers:

k0ka [10]4 years ago

4 0

There are infinitely many solutions

timurjin [86]4 years ago

3 0

Answer:

<em>There are infinitely many solutions.</em>

Step-by-step explanation:

<em>While solving a system of equations, if we get a true statement like 1=1, then there will be "infinitely many solutions" and if we get a false statement like 1=2, then there will be "no solution". </em>

Here the statement is 4=4, <u>which is a true statement</u>.

So, there are infinitely many solutions.

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Rewrite without absolute value for the given conditions: y=|x−5|+|x+5|, if x>5

julia-pushkina [17]

Answer:

$y=2x$ if $x>5$

Problem:

"Rewrite without absolute value for the given conditions: y=|x−5|+|x+5|, if x>5"

Step-by-step explanation:

Let's figure out when the insides of the absolute values are positive and negative, and then see where the given condition that x>5 fits into that.

$|x-5|=x-5$ if $x-5$ is positive or 0, $\ge 0$ .

$x-5 \ge 0$

Add 5 on both sides:

$x \ge 5$ .

$|x-5|=-(x-5)$ if $x-5$ is negative or zero, $\le 0$ .

$x-5 \le 0$

Add 5 on both sides:

$x \le 5$

Since $x>5$ then we will choose $|x-5|=x-5$ .

---

$|x+5|=x+5$ if $x+5$ is positive or 0, $\ge 0$ .

$x+5 \ge 0$

Subtract 5 on both sides:

$x \ge -5$ .

$|x+5|=-(x+5)$ if $x+5$ is negative or zero, $\le 0$ .

$x+5 \le 0$

Subtract 5 on both sides:

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Since $x>5$ then we will choose $|x+5|=x+5$ .

--

$y=|x−5|+|x+5|$ with $x>5$ :

$y=(x-5)+(x+5)$

$y=(x+x)+(-5+5)$

$y=(2x)+(0)$

$y=2x+0$

$y=2x$

6 0

3 years ago