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zmey [24]
3 years ago
11

Solve the following system using the substitution, elimination, or graphing method for the x coordinate:

Mathematics
1 answer:
igomit [66]3 years ago
3 0
Hey there!

To solve this system of equations, you will need to get one of the terms in both equations to cancel out to zero. If there isn't a term that you can cancel out, you can multiply either or both equations to make that term. There's no wrong way to do this, just as long as you make sure that you double check whether your should add or subtract. This is easier shown than explained, so refer below:

<span>  x + y = +1
5x + y = –6

</span>–1(x + y = +1)
   5x + y = –6

–x – y = –1
5x + y = –6

You can see that once we combine these equations by adding, the y term will become 0, eliminating it. This is necessary for solving the system, so make sure you do it. Also, remember to distribute the term that you need to to all of the numbers in the equation! After that, just solve for the variable that's still in the equation. 

   –x – y = –1
+ 5x + y = –6

4x + 0y = –7
4x = –7
x = –1.75

Now, just plug the value we found for x into either one of your equations in the original system as it's presented in your problem. 

x + y = 1
–1.75 + y = 1
+1.75        +1.75

y = 2.75

All that's left to do is check your point (–1.75, 2.75). If it's true for both equations, your answer is correct!

–1.75 + 2.75 = 1
<span>5(–1.75) + 2.75 = –6

</span>(–1.75, 2.75) is the solution to your system. 

Hope this helped you out! :-)
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two coplanar lines that are perpendicular to the same line are parallel. a) always b) sometimes c) never
sergeinik [125]

<u>Answer:</u>

Two co planar lines that are perpendicular to the same line are always PARALLEL. So option A is correct.

<u>Explanation:</u>

Given:

  • Two lines are coplanar.
  • They are perpendicular to the same line  

To find:

whether they are parallel or not and choose the correct option from the given options.

Solution:

Now, we know that, slopes of perpendicular lines is -1

Then, \text{{slope of 1st line}}\times \text{{slope of perpendicular line}} = -1

\text{{slope of perpendicular line}} =\frac{- 1}{\text{{1st line slope}}}

similarly

\text{{slope of 2st line}}\times \text{{slope of perpendicular line}} = -1

\text{{slope of perpendicular line}} =\frac{- 1}{\text{{2st line slope}}}

Now, as both lines are perpendicular to same line, then, we have to equate above both of them.

Then, \frac{- 1}{\text{{1st line slope}}}= \frac{-1 }{\text{{2nd line slope}}}

1st line slope = 2nd line slope

Here, slopes of two lines are equal.

Hence, Two coplanar lines that are perpendicular to the same line are always parallel. So option A is correct.

6 0
3 years ago
<img src="https://tex.z-dn.net/?f=7.5d%20%2B%2085%20%3D%20130" id="TexFormula1" title="7.5d + 85 = 130" alt="7.5d + 85 = 130" al
Stella [2.4K]
Hello there!

To solve for the variable of d, the first thing you must do is to subtract over any constants in order to isolate the term with the variable in it.

In this case, you would subtract 85 from both sides:
7.5d+85-85=130-85

When this simplifies, you should get:
7.5d=45

Now, divide both sides by 7.5 to isolate d:
7.5d/7.5=45/7.5

This would result in your answer, d=6

To check if this is correct, plug 6 back into the original equation to see if you result in 130=130:
7.5(6)+85=130
45+85=130
130=130

Hope this helps!
3 0
3 years ago
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