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erica [24]
3 years ago
12

to start to solve the system of equations below, which number would you multiply in the equation -2x-5y=-1? The two equations ar

e -2x-5y=-1 and 4x+2y=8
Mathematics
1 answer:
Leviafan [203]3 years ago
5 0

Answer:

  The first equation can be multiplied by 2.

Step-by-step explanation:

The x-coefficients are -2 and 4. If the first one of these is multiplied by 2, it will be the opposite of the second of these. That is 2·(-2) = -4. When -4 and 4 are added, the result is 0, so the x-variable will be eliminated.

To solve these equations by "elimination", you look for simple relationships between the coefficients that will let you combine them to get zero.

_____

Here's the rest of the solution.

  2(-2x-5y) +(4x+2y) = 2(-1) +(8) . . . . after multiplying the first equation by 2 and adding the second equation

  -4x -10y +4x +2y = -2 +8 . . . . . the result of eliminating parentheses

  -8y = 6 . . . . . the result of collecting terms

  y = -6/8 = -3/4 . . . . divide by the y-coefficient

Since all of the coefficients in the second equation are even, a factor of 2 can be removed, and the equation written as ...

   2x +y = 4

This can be solved for x, so you have ...

  x = (4 -y)/2 = 2 -(y/2)

Filling in the above value of y, we find x to be ...

  x = 2 -(-3/4)/2

  x = 2 3/8

_____

<em>Comment on eliminating y instead of x</em>

If you divide the second equation by 2 so that y has a coefficient of 1, then you can multiply this equation by 5 to give y a coefficient that is the opposite of the coefficient -5 in the first equation. Then the elimination looks like

  (-2x -5y) +5(2x +y) = (-1) +5(4)

  -2x -5y +10x +5y = -1 +20 . . . . eliminate parentheses

  8x = 19 . . . . simplify

  x = 19/8 = 2 3/8 . . . . divide by the coefficient of x

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IrinaK [193]

Answer:

Equation of the circle   (x-3)²+(y-5)²=(6.4)²

                             x² -6x +9 +y² -10y +25 = 40.96

Step-by-step explanation:

<u><em>Step(i):-</em></u>

Given endpoints of diameter P(−2, 1) and Q(8, 9)

Centre of circle = midpoint of diameter

                   Centre = (\frac{-2+8}{2} ,\frac{1+9}{2} )

               Centre (h, k) = (3 , 5)

<u><em>Step(ii):-</em></u>

The distance of two end points

PQ = \sqrt{(x_{2}-x_{1} )^{2} +(y_{2} -y_{1} )^{2}  }

PQ= \sqrt{(8+2 )^{2} +(8 )^{2}  }

PQ = √164 = 12.8

Diameter    d = 2r

                 radius r = d/2

                Radius r = 6.4

<u><em>Final answer:-</em></u>

Equation of the circle  

                    (x-h)²+(y-k)² = r²

                   (x-3)²+(y-5)²=(6.4)²

x² -6x +9 +y² -10y +25 = 40.96

x² -6x  +y² -10y  = 40.96-34

x² -6x  +y² -10y -7= 0

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Answer:

a = - 4, b = 5

Step-by-step explanation:

Expand the left side and compare the coefficients of like terms on the right side.

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Comparing like terms with - 6x² + 12x - 15

x - term → - 3a = 12 ( divide both sides by - 3 )

                    a = - 4

constant term → - 3b = - 15 ( divide both sides by - 3 )

                               b = 5

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