Systems of equations, help please?

Mathematics

1 answer:

lord [1]3 years ago

3 0

4x + 3y = 54 (1)
3x + 9y = 108 (2)

Multiply (1) by (-3)
-12x - 9y = -162
3x + 9y = 108
---------------------add
-9x = -54
x = 6

plug x = 6 into (1) to find y
4(6) + 3y = 54
24 + 3y = 54
3y = 30
y = 10

Answer
(6 , 10)

Hope it helps.

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One Friday night, two large groups of people called Centerville Taxi Service. The first group

NeX [460]

Answer:sedan can hold 3 people and a minivan can hold 9 people.

Step-by-step explanation:

Suppose the number of passengers each sedan can carry is A and the number of passengers each minivan can carry is B

So 3A + 2B = 21 and 3A + 3B = 27

If we subtract the equations we can solve for B

3A + 3B = 27

-3A - 2B = 21

___________

B = 6

Now we know Each minivan can hold 6 passengers and we can solve for A.

3A + 3B = 27

3A + 3(6) = 27

3A + 18 = 27

- 18. -18

__________

3A = 9

A =3

You can check this by solving the other equation.

3A + 2B = 21

3(3) + 2(6) = 21

9 + 12 = 21

Hope that helps

4 0

2 years ago

Given vectors u = (-3,2) and v = (4,-1), if vector w=2u -3v, what is ||w|| ?

Brums [2.3K]

$\bf \begin{cases}
u=\ \textless \ -3,2\ \textgreater \ \\
2u=2\ \textless \ -3,2\ \textgreater \ \\
\qquad \ \textless \ 2\cdot -3,2\cdot 2\ \textgreater \ \\
\qquad \boxed{\ \textless \ -6,4\ \textgreater \ }\\
----------\\
v=\ \textless \ 4,-1\ \textgreater \ \\
3v=3\ \textless \ 4,-1\ \textgreater \ \\
\qquad \ \textless \ 3\cdot 4,3\cdot -1\ \textgreater \ \\
\qquad \boxed{\ \textless \ 12,-3\ \textgreater \ }
\end{cases}\qquad
\begin{array}{llll}
w=2u-3v\\\\
w=\ \textless \ -6,4\ \textgreater \ -\ \textless \ 12,-3\ \textgreater \ \\\\
w=\ \textless \ -6-12,4-(-3)\ \textgreater \ \\\\
w=\ \textless \ -18,4+3\ \textgreater \ \\\\
\boxed{w=\ \textless \ -18,7\ \textgreater \ }
\end{array}
\\\\\\
||w||\implies \sqrt{a^2+b^2}\implies ||w||=\sqrt{(-18)^2+(7)^2}\implies ||w||=373$