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Maru [420]
3 years ago
5

Find the solution of the system of equations.6x + 8y = -8x + 4y = 4( , )​

Mathematics
1 answer:
ladessa [460]3 years ago
8 0

Answer:

the solution is (-4, 2)

Step-by-step explanation:

6x + 8y = -8

x + 4y = 4

... can be solved using elimination by addition and subtraction, among other methods.  Multiply the second equation by -2 to obtain

6x + 8y = -8

-2x - 8y = -8

Combining these results in

4x = -16.  Thus, x = -4.

Substituting -4 for x in x + 4y = 4 results in

-4 + 4y = 4, or 4y = 8, or y = 2

Then the solution is (-4, 2)

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Find the point(s) of intersection (if any) of the plane and the line. Also, determine whether the line lies in the plane. 2x - 2
s2008m [1.1K]

Answer:

the intersection is the point P=(x,y,z)=(8,9,14) and the line does not lie in the plane

Step-by-step explanation:

from the equation of the line

x - 1/2 = y + (3/2)/-1 = (z + 1) / 2  = t (parameter)

then the parametric equation of the line is

x= 1/2 +t

y =  (3/2) + t

z = (-1) + 2*t

therefore from the equation of the plane

2x - 2y + z = 12

2*(1/2 +t) - 2[(3/2) + t]  + [(-1) + 2*t]  = 12

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t= 15/2

therefore there is only one intersection of the line with the plane ( then the line does not lie in the plane , since there would be infinite intersection points). The intersection is

x= 1/2 +t = 1/2 +15/2 = 8

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