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Sever21 [200]
1 year ago
5

← How many solutions does this linear system have y = x+2 6x - 4y = -10

Mathematics
1 answer:
defon1 year ago
8 0

Answer:

This linear system has one solution.

Step-by-step explanation:

First equation: y = x + 2

Second equation: 6x - 4y = -10

Let's change the second equation in slope-intercept form y = mx + b.

<u>Slope-intercept form</u>

y = mx + b

m ... slope

b ... y-intercept

6x - 4y = -10

6x + 10 = 4y

\frac{6}{4}x + \frac{10}{4} = y

\frac{3}{2}x + \frac{5}{2} = y

If two lines have the <em>same slope </em>but <em>different y-intercept</em>, they are parallel - <u>system has no solutions</u>.

If two lines have the <em>same slope</em> and the <em>same y-intercept</em>, they are the same line and are intersecting in infinite many points - <u>system has infinite many solutions</u>.

If two lines have <em>different slopes</em> then they intersect in one point - <u>system has one solution</u>.

We see that lines have different slopes. First line has slope 1 and the other line has slope \frac{3}{2}. So the system has one solution.

You can also check this by solving the system.

Substitute y in second equation with y from first.

6x - 4y = -10

6x - 4(x + 2) = -10

Solve for x.

6x - 4x - 8 = -10

2x = -2

x = -1

y = x + 2

y = -1 + 2

y = 1

The lines intersect in point (-1, 1). <-- one solution

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If it took 6 hours to clean 12 houses, how many houses could be cleaned in 11 hours?
nata0808 [166]

22 houses can be cleaned in 11 hours.

Step-by-step explanation:

It is given that;

6 hours = 12 houses cleaned

1 hour = \frac{12}{6}\ houses\ cleaned\\

1 hour = 2 houses cleaned

In 1 hour, 2 houses can be cleaned, therefore,

11 hours = Time*houses cleaned in one hour

11 hours = 11*2 =22 houses cleaned

22 houses can be cleaned in 11 hours.

Keywords: unit rate, multiplication

Learn more about multiplication at:

  • brainly.com/question/7932185
  • brainly.com/question/8054589

#LearnwithBrainly

6 0
3 years ago
I need to know what m n and q are equal to
VMariaS [17]
I know m=2.25 and n=8.6 but I don't know about q.
3 0
3 years ago
PLEASE HELP ME!!!!!!!!!!!!!!!
Vinil7 [7]

Answer:

The last one

Step-by-step explanation:

4 0
3 years ago
Question. 1 :
vovikov84 [41]
<h3>Answer to Question 1:</h3>

AB= 24cm

BC = 7cm

<B = 90°

AC = ?

<h3>Using Pythagoras theorem :-</h3>

AC^2 = AB^2 + BC ^ 2

AC^2 = 24^2 + 7^2

AC^2 = 576 + 49

AC^2 = √625

AC = 25

<h3>Answer to Question 2 :-</h3>

sin A = 3/4

CosA = ?

TanA = ?

<h3>SinA = Opp. side/Hypotenuse</h3><h3> = 3/4</h3>

(Construct a triangle right angled at B with one side BC of 3cm and hypotenuse AC of 4cm.)

<h3>Using Pythagoras theorem :-</h3>

AC^2 = AB^2 + BC ^ 2

4² = AB² + 3²

16 = AB + 9

AB = √7cm

<h3>CosA = Adjacent side/Hypotenuse</h3>

= AB/AC

= √7/4

<h3>TanA= Opp. side/Adjacent side</h3>

=BC/AB

= 3/√7

4 0
2 years ago
How much money does Conor earn each minute he does yard work, if he works 3.25 hours at $9 an hour?
LenaWriter [7]

Answer:

$2.76

Step-by-step explanation:

9/3.25=2.76

8 0
3 years ago
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