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Vlad [161]
3 years ago
15

Graph the system of equations. −x+2y=−8 3x−y=−6

Mathematics
2 answers:
BARSIC [14]3 years ago
7 0

Answer: x = - 4

y = - 6

Step-by-step explanation:

The given system of linear equations is expressed as

- x + 2y = - 8- - - - - - - - - - - - -1

3x - y = - 6 - - - - - - - - - - - -2

We would eliminate x by multiplying equation 1 by 3 and equation 2 by 1. It becomes

- 3x + 6y = - 24- - - - - - - - - - -3

3x - y = - 6- - - - - - - - - - - -4

Adding equation 3 to equation 4, it becomes

5y = - 30

Dividing the left hand side and the right hand side of the equation by 3, it becomes

5y/5 = - 30/5

y = - 6

Substituting y = - 6 into equation 2, it becomes

3x - - 6 = - 6

3x + 6 =- 6

Subtracting 6 from the left hand side and the right hand side of the equation, it becomes

3x + 6 - 6 = - 6 - 6

3x = - 12

Dividing the left hand side and the right hand side of the equation by 3, it becomes

3x/3 = - 12/3

x = - 4

Evgen [1.6K]3 years ago
6 0

Answer:

x = -4, y = -6

Step-by-step explanation:

-x+2y = -8

3x-y = -6

x = 2y+8

3(2y+8) - y = -6

6y + 24 -y = -6

5y = -30

y = -6

x = 2(-6)+8 = -12+8 = -4

x = -4, y = -6

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LOTS OF POINTS GIVING BRAINLIEST I NEED HELP PLEASEE
Sidana [21]

Answer:

Segment EF: y = -x + 8

Segment BC: y = -x + 2

Step-by-step explanation:

Given the two similar right triangles, ΔABC and ΔDEF, for which we must determine the slope-intercept form of the side of ΔDEF that is parallel to segment BC.

Upon observing the given diagram, we can infer the following corresponding sides:

\displaystyle\mathsf{\overline{BC}\:\: and\:\:\overline{EF}}

\displaystyle\mathsf{\overline{BA}\:\: and\:\:\overline{ED}}

\displaystyle\mathsf{\overline{AC}\:\: and\:\:\overline{DF}}

We must determine the slope of segment BC from ΔABC, which corresponds to segment EF from ΔDEF.

<h2>Slope of Segment BC:</h2>

In order to solve for the slope of segment BC, we can use the following slope formula:

\displaystyle\mathsf{Slope\:(m)\:=\:\frac{y_2 \:-\:y_1}{x_2 \:-\:x_1}}  }

Use the following coordinates from the given diagram:

Point B:  (x₁, y₁) =  (-2, 4)

Point C:  (x₂, y₂) = ( 1,  1 )

Substitute these values into the slope formula:

\displaystyle\mathsf{Slope\:(m)\:=\:\frac{y_2 \:-\:y_1}{x_2 \:-\:x_1}}\:=\:\frac{1\:-\:4}{1\:-\:(-2)}\:=\:\frac{-3}{1\:+\:2}\:=\:\frac{-3}{3}\:=\:-1}

<h2>Slope of Segment EF:</h2>

Similar to how we determined the slope of segment BC, we will use the coordinates of points E and F from ΔDEF to find its slope:

Point E:  (x₁, y₁) =  (4, 4)

Point F:  (x₂, y₂) = (6, 2)

Substitute these values into the slope formula:

\displaystyle\mathsf{Slope\:(m)\:=\:\frac{y_2 \:-\:y_1}{x_2 \:-\:x_1}}\:=\:\frac{2\:-\:4}{6\:-\:4}\:=\:\frac{-2}{2}\:=\:-1}

Our calculations show that segment BC and EF have the same slope of -1.  In geometry, we know that two nonvertical lines are <u>parallel</u> if and only if they have the same slope.  

Since segments BC and EF have the same slope, then it means that  \displaystyle\mathsf{\overline{BC}\:\: | |\:\:\overline{EF}}.

<h2>Slope-intercept form:</h2><h3><u>Segment BC:</u></h3>

The <u>y-intercept</u> is the point on the graph where it crosses the y-axis. Thus, it is the value of "y" when x = 0.

Using the slope of segment BC, m = -1, and the coordinates of point C, (1,  1), substitute these values into the <u>slope-intercept form</u> (y = mx + b) to solve for the y-intercept, <em>b. </em>

y = mx + b

1 = -1( 1 ) + b

1 = -1 + b

Add 1 to both sides to isolate b:

1 + 1 = -1 + 1 + b

2 = b

Hence, the <u><em>y-intercept</em></u> of segment BC is: <em>b</em> = 2.

Therefore, the linear equation in <u>slope-intercept form of segment BC</u> is:

⇒  y = -x + 2.

<h3><u /></h3><h3><u>Segment EF:</u></h3>

Using the slope of segment EF, <em>m</em> = -1, and the coordinates of point E, (4, 4), substitute these values into the <u>slope-intercept form</u> to solve for the y-intercept, <em>b. </em>

y = mx + b

4 = -1( 4 ) + b

4 = -4 + b

Add 4 to both sides to isolate b:

4 + 4 = -4 + 4 + b

8 = b

Hence, the <u><em>y-intercept</em></u> of segment BC is: <em>b</em> = 8.

Therefore, the linear equation in <u>slope-intercept form of segment EF</u> is:

⇒  y = -x + 8.

8 0
2 years ago
The Smith family went to eat at Buffalo Wild Wings. The bill was $43.86. They gave the server a 20% tip. How much did they pay a
Marysya12 [62]
<h2>Answer:</h2>

$52.63

<h2>Step-by-step explanation:</h2>

To find 20% of $43.86 we multiply $43.86 by 0.2

$43.86 • 0.2 = $8.772

Now add $43.86 and $8.772 to find out how much the family paid altogether.

$43.86 + $8.772 = $52.632

In money the smallest place value is cents so we have to round to the hundredths place.

Doing this we get the grand answer of:

$52.63

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Slope= -5
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The unit rate is 2.17
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