7x - y = - 1 + -7x + 3y = - 25

1 answer:

4 0

Hope this helps you out :D

It’s 2 equations so in order to solve the previous system, you can use different methods, as for example substitution or addition of equations. In this case, you use the second one, due to the fact you have 7x in one equation and -7x in the other equation. In this way you can easily eliminate variable x and then solve for y. With the value of y you can replace in any of the two equations and solve for x.

7x-y=-1
-7x+3y=-25

Summarizing, you proceed as follow:
- add up the given equations

7x - y = -1

-7x+3y=-25
——————
0 +2y=-26

- solve for y in the previous equation

2y=-26
y=-26/2
y=-13

- replace the obtained value of y in one of the given equations, and solve for x

7x-(-13)=-1

7x+13=-1

7x=-1-13

7x=-14

x=-14

x=-14/7

x=-2

Hence, the solution of the given systems of equation is:

X=-2

Y=-13

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2 years ago

Find the directional derivative of f(x,y,z)=2z2x+y3f(x,y,z)=2z2x+y3 at the point (−1,4,3)(−1,4,3) in the direction of the vector

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$f(x,y,z)=2z^2x+y^3$

$f$ has gradient

$\nabla f(x,y,z)=2z^2\,\vec\imath+3y^2\,\vec\jmath+4xz\,\vec k$

which at the point (-1, 4, 3) has a value of

$\nabla f(-1,4,3)=18\,\vec\imath+48\,\vec\jmath-12\,\vec k$

I'm not sure what the given direction vector is supposed to be, but my best guess is that it's intended to say $\vec u=15\,\vec\imath+25\,\vec\jmath$ , in which case we have