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Arisa [49]
3 years ago
13

What does it mean for a point to be the solution to two equations​

Mathematics
1 answer:
Hunter-Best [27]3 years ago
4 0

Answer:

It means the point will satisfy both the equations.

Step-by-step explanation:

If we consider a point P(x_{1},y_{1}) which is the solution of two equations ax + by + c = 0 and px + qy + r = 0, then it conveys the information that both the equations will be satisfied by this point.

That means ax_{1} + by_{1} + c = 0 and px_{1} + qy_{1} + r = 0

At the same time if we consider the geometric interpretation then, the graph of the equations ax + by + c = 0 and px + qy + r = 0 will always pass through the common point P(x_{1},y_{1}).  (Answer)

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1. 3x + 12 = 8x - 18
Ray Of Light [21]

Answer:

  1. given
  2. addition property of equality
  3. addition property of equality
  4. division property of equality
  5. symmetric property of equality

Step-by-step explanation:

In step 2, -3x was added to both sides in accordance with the addition property of equality.

The same property lets you add 18 to both sides, as in step 3.

The division property of equality lets you divide both sides of the equation by 5. (Or, the multiplication property lets you multiply by 1/5.)

Swapping sides of the equal sign is allowed by the symmetric property of equality.

5 0
3 years ago
7b + 3 – 4b = 3 – 3(b + 4)
svlad2 [7]

Hello from MrBillDoesMath!

Answer:  b

Discussion:

7b + 3 - 4b = 3 - 3(b+4)  =>

7b + 3 - 4b = 3 - 3b -12 =>

(7b - 4b) + 3   = -3b - 9 =>

3b + 3 = -3b -9    =>      Add 9 to both sides

3b + 12 = -3b -9 + 9  =>

3b + 12 = -3b  =>         ( add 3b to both sides)

6b + 12 = 0 =>             (subtract 12 from both sides)

6b = -12 =>

b = -12/6 = -2


Thank you,

MrB


7 0
3 years ago
Find dy/dx by implicit differentiation.
kow [346]

dy/dx by implicit differentiation is cos(πx)/sin(πy)

<h3>How to find dy/dx by implicit differentiation?</h3>

Since we have the equation

(sin(πx) + cos(πy)⁸ = 17, to find dy/dx, we differentiate implicitly.

So, [(sin(πx) + cos(πy)⁸ = 17]

d[(sin(πx) + cos(πy)⁸]/dx = d17/dx

d[(sin(πx) + cos(πy)⁸]/dx = 0

Let sin(πx) + cos(πy) = u

So, du⁸/dx = 0

du⁸/du × du/dx = 0

Since,

  • du⁸/du = 8u⁷ and
  • du/dx = d[sin(πx) + cos(πy)]/dx

= dsin(πx)/dx + dcos(πy)/dx

= dsin(πx)/dx + (dcos(πy)/dy × dy/dx)

= πcos(πx) - πsin(πy) × dy/dx

So, du⁸/dx = 0

du⁸/du × du/dx = 0

8u⁷ × [ πcos(πx) - πsin(πy) × dy/dx] = 0

8[(sin(πx) + cos(πy)]⁷ ×  (πcos(πx) - πsin(πy) × dy/dx) = 0

Since 8[(sin(πx) + cos(πy)]⁷ ≠ 0

(πcos(πx) - πsin(πy) × dy/dx) = 0

πcos(πx) = πsin(πy) × dy/dx

dy/dx = πcos(πx)/πsin(πy)

dy/dx = cos(πx)/sin(πy)

So, dy/dx by implicit differentiation is cos(πx)/sin(πy)

Learn more about implicit differentiation here:

brainly.com/question/25081524

#SPJ1

6 0
2 years ago
Factor the question: 4x+8y+16
kirill [66]
Y= - X/2 = 2 this is the answer
8 0
2 years ago
Order these values from smallest (A) to largest (F)
Flauer [41]
We need the values to answer this question
6 0
3 years ago
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