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3 years ago

Solve the system of equations by substitution.

Mathematics

1 answer:

mojhsa [17]3 years ago

6 0

Answer:

6 = −4x + y

−5x − y = 21

Answer: (-3, -6)

2x + y = 20 6x – 5y = 12

Answer:

(7 , 6)

Step-by-step explanation:

Solve the system of equations by substitution.

6 = −4x + y --> y = 4x + 6

−5x − y = 21

Substitute y = 4x + 6 into −5x − y = 21

−5x − (4x + 6) = 21

-5x - 4x - 6 = 21

-9x = 27

x = - 3

y = 4(-3) + 6

y = -12 + 6

y = -6

(-3, -6)

Solve the system by the elimination method.

2x + y = 20

multiply the equation by (-3) ; 2x + y = 20 so

-6x - 3y = - 60

6x – 5y = 12

------------------add

-8y = - 48

y = 6

2x + y = 20

2x + 6 = 20

2x = 14

x = 7

(7 , 6)

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4 years ago

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Quadrilateral KLMN is a rectangle. The coordinates of L are L(1,-4), and the coordinates of Mare M(3,-2). Find the slopes of sid

lozanna [386]

L(1, -4)=(xL, yL)→xL=1, yL=-4
M(3, -2)=(xM, yM)→xM=3, yM=-2

Slope of side LM: m LM = (yM-yL) / (xM-xL)
m LM = ( -2 - (-4) ) / (3-1)
m LM = ( -2+4) / (2)
m LM = (2) / (2)
m LM = 1

The quadrilateral is the rectangle KLMN
The oposite sides are: LM with NK, and KL with NK
In a rectangle the opposite sides are parallel, and parallel lines have the same slope, then:
Slope of side LM = m LM = 1 = m NK = Slope of side NK
Slope of side NK = m NK = 1

Slope of side KL = m KL = m MN = Slope of side MN

The sides KL and LM (consecutive sides) are perpendicular (form an angle of 90°), then the product of their slopes is equal to -1:
(m KL) (m LM) = -1
Replacing m LM = 1
(m KL) (1) = -1
m KL = -1 = m MN

Answer:
Slope of side LM =1
Slope of side NK =1
Slope of side KL = -1
Slope of side MN = -1

3 0

3 years ago

HELP PLEASE ASAP:

VashaNatasha [74]

The average rate of change, of the function, between the intervals, x = 2 to x = 6 is: 180.

<h3>What is the Average Rate of Change of a Function?</h3>

Average rate of change = $\frac{f(b) - f(a)}{b - a}$ .