Step-by-step explanation:
The answer is 10
First calculate one side the answer is 70 now you have to find such a number that when you multiply it both sides are equal
(7) × 10 = (5 ×_) + 20
70 = (5 × 10) + 20
70 = 50 +20
70 = 70
A set of vectors {v1,v2,...,vk} is linearly independent if the vector equation x1v1 + x2v2 + .......... + xkvk = 0 has only the trivial solution
x1 = x2 = .... = xk =0. Then the set {v1,v2,...,vk} is linearly dependent otherwise.
So putting in the formula we get
x1u1 + x2u2 + x3u3 = 0
x1u1 + x2u2 = -x3u3
au1 + bu2 = u3 ∵ (-x1/x3 = a & -x2/x3 = b)
On putting in the values
a(3,-1) + b(4,5) = (-4,7)
(3a+4b,-a+5b) = (-4,7)
On comparing we get
3a + 4b = -4 -(1)
-a + 5b = 7 -(2)
on solving these equations we get
b = 17/19 and a= -48/19
which is non trivial.
Thus the following form linearly dependent sets of vectors.
Learn more about linear dependence of vectors here :
brainly.com/question/13776214
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Equation 1) 5x + 3y = 16
Equation 2) 3x - 5y = -4
Multiply all of equation 1 by 3, and all of equation 2 by 5.
1) 3(5x+3y=16)
2) 5(3x-5y=-4)
Simplify.
1) 15x + 9y = 48
2) 15x - 25y = -20
Subtract equations from each other.
34y = 68
Divide both sides by 34.
y = 2
Plug in 2 for y in first equation.
5x + 3y = 16
5x + 3(2) = 16
Simplify.
5x + 6 = 16
Subtract 6 from both sides.
5x = 10
Divide both sides by 5.
x = 2
(2, 2)
~Hope I helped!~