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Vlad [161]
3 years ago
7

What is the solution to the system of equations? 3x-6y=-12 " " x-2y=10 Use the substitution method to justify that the given sys

tem of equations has no solution. What do you know about the two lines in this system of equations?
Mathematics
1 answer:
Thepotemich [5.8K]3 years ago
6 0

The two lines in this system of equations are parallel

Step-by-step explanation:

Let us revise the relation between 2 lines

  • If the system of linear equations has one solution, then the two line are intersected
  • If the system of linear equations has no solution, then the two line are parallel
  • If the system of linear equations has many solutions, then the two line are coincide (over each other)

∵ The system of equation is

3x - 6y = -12 ⇒ (1)

x - 2y = 10 ⇒ (2)

To solve the system using the substitution method, find x in terms of y in equation (2)

∵ x - 2y = 10

- Add 2y to both sides

∴ x = 2y + 10 ⇒ (3)

Substitute x in equation (1) by equation (3)

∵ 3(2y + 10) - 6y = -12

- Simplify the left hand side

∴ 6y + 30 - 6y = -12

- Add like terms in the left hand side

∴ 30 = -12

∴ The left hand side ≠ the right hand side

∴ There is no solution for the system of equations

∴ The system of equations represents two parallel lines

The two lines in this system of equations are parallel

Learn more:

You can learn more about the equations of parallel lines in brainly.com/question/8628615

#LearnwithBrainly

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200 is 10 times as much as blank and 1 tenth of
anzhelika [568]

Answer:

200 is 10 times as much as 20 and 1 tenth of 2,000

Step-by-step explanation:

Divide 200 by 10 and you'll get 20 and multiply it by 10 to get 2,000.

8 0
3 years ago
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Ill give you alot of points for this
rusak2 [61]

Answer:

ok

Step-by-step explanation:

4 0
3 years ago
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Stuart's bank account had a balance of - $54.19 last month. This month he won a cash prize of $70.82 for winning a competition.
Alenkinab [10]

If Stuart starts with -$54.19 then gains $70.82, you have to add the gained amount to the origin amount. Since the origin amount is negative, you can also subtract the origin amount from the gained amount to find the amount left at the end of the month.

Add 70.82 to -54.19

-54.19 + 70.82 = 16.63

<u>Alternative method:</u>

First, subtract 54.19 from 70.82.

70.82 - 54.19 = 16.63

Add 54.19 to -54.19, bringing you to 0.

-54.19 + 54.19 = 0

Now add the remaining 16.63.

0 + 16.63 = 16.63

<h2>Answer:</h2>

<u>Stuart will have </u><u>$16.63</u><u> at the end of this month.</u>

7 0
2 years ago
What is different between solving inequalities and absolute value inequalities?
Ivenika [448]

Answer:

The absolute number of a number a is written as

|a|

And represents the distance between a and 0 on a number line.

An absolute value equation is an equation that contains an absolute value expression. The equation

|x|=a

Has two solutions x = a and x = -a because both numbers are at the distance a from 0.

To solve an absolute value equation as

|x+7|=14

You begin by making it into two separate equations and then solving them separately.

x+7=14

x+7−7=14−7

x=7

or

x+7=−14

x+7−7=−14−7

x=−21

An absolute value equation has no solution if the absolute value expression equals a negative number since an absolute value can never be negative.

The inequality

|x|<2

Represents the distance between x and 0 that is less than 2

Whereas the inequality

|x|>2

Represents the distance between x and 0 that is greater than 2

You can write an absolute value inequality as a compound inequality.

−2<x<2

This holds true for all absolute value inequalities.

|ax+b|<c,wherec>0

=−c<ax+b<c

|ax+b|>c,wherec>0

=ax+b<−corax+b>c

You can replace > above with ≥ and < with ≤.

When solving an absolute value inequality it's necessary to first isolate the absolute value expression on one side of the inequality before solving the inequality.

Step-by-step explanation:

Hope this helps :)

5 0
3 years ago
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Help I need to turn this in by 12:30
11Alexandr11 [23.1K]
B- -3

If x is two according to the coordinate points, that means the equation is now -8+3y=-17

Add 8 to each side- 3y=-9

And divide -9 by 3

This gets you y=-3
5 0
2 years ago
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