All categories

3 years ago

Solve: 8x+14y=4 6x+7y=10

Mathematics

1 answer:

Anarel [89]3 years ago

7 0

Answer:

Therefore, x = 4 and y = -2.

Step-by-step explanation:

The steps are ;

$8x + 14y = 4$

$2(4x + 7y) = 4$

$4x + 7y = 2 - - - (1)$

$6x + 7y = 10 - - - (2)$

$(2) - (1)$

$6x - 4x = 10 - 2$

$2x = 8$

$x = 4$

$sub \: x = 4 \: into \: (1)$

$(1)⇒$

$4(4) + 7y = 2$

$16 + 7y = 2$

$7y = - 14$

$y = - 2$

You might be interested in

An electronics company produces transistors, resistors, and computer chips. Each transistor requires 3 units of copper, 2 unit

Gala2k [10]

Answer:

475 transistors, 25 resistors and 50 computer chips can be produced.

Step-by-step explanation:

Let us consider, p = Number of transistors.

q = Number of resistors.

r = Number of computer chips.

The following three linear equations according to question,

$3\times p + 3\times q + 2\times r = 1600\\2\times p + 1\times q + 1\times r = 1025\\1\times p + 2\times q + 2\times r = 625$

The matrix form of any system, Ax = B

Where, A = Coefficient matrix

B = Constant vector

x = Variable vector

$A = \left[\begin{array}{ccc}3&3&2\\2&1&1\\1&2&2\end{array}\right], x = \left[\begin{array}{ccc}p\\q\\r\end{array}\right], B = \left[\begin{array}{ccc}1600\\1025\\625\end{array}\right]$

The inverse matrix, $A^{-1}$ can be found by using the following formula,

$A^{-1} = \frac{1}{det A}\times (C_{A}) ^{T}$

Where, det A = Determinant of matrix A.

$C_{A}$ = Matrix of cofactors of A

Now, applying this formula to find $A^{-1}$ ;

$det A = \left[\begin{array}{ccc}3&3&2\\2&1&1\\1&2&2\end{array}\right] = 3\times(2-2)-3\times(4-1)+2\times(4-1) = -3$

Here, $det A\neq 0$ , thus the matrix is invertible.

$C_{A} = \left[\begin{array}{ccc}(2-2)&-(4-1)&(4-1)\\-(6-4)&(6-2)&-(6-3)\\(3-2)&-(3-4)&(3-6)\end{array}\right] = \left[\begin{array}{ccc}0&-3&3\\-2&4&-3\\1&1&-3\end{array}\right] \\(C_{A}) ^{T} = \left[\begin{array}{ccc}0&-3&3\\-2&4&-3\\1&1&-3\end{array}\right] ^{T} = \left[\begin{array}{ccc}0&-2&1\\-3&4&1\\3&-3&-3\end{array}\right]$

$A^{-1} = \frac{1}{-3}\times\left[\begin{array}{ccc}0&-2&1\\-3&4&1\\3&-3&-3\end{array}\right] \\ So, x= \frac{1}{-3} \left[\begin{array}{ccc}0&-2&1\\-3&4&1\\3&-3&-3\end{array}\right]\times\left[\begin{array}{ccc}1600\\1025\\625\end{array}\right]= \frac{1}{-3} \left[\begin{array}{ccc}-1425\\-75\\-150\end{array}\right] = \left[\begin{array}{ccc}475\\25\\50\end{array}\right]$

So, p = 475, q = 25, r = 50.

7 0

3 years ago

This table shows the number Carol and Anna walked each day for 5 days.

Alex787 [66]

Answer:

Step-by-step explanation:

6 0

3 years ago

Rico thinks of a number between 30 and 40 that is represented by

Anna007 [38]

Hello,

x,y,z∈ IN

$x=\frac{3}{4}*y$
$y=\frac{1}{3}*z$

$140$
$46\leq\ y\ \leq\ 50 ==>\ \frac{46*3}{4}\leq\frac{3y}{4}\leq\frac{50*3}{4}$
$35\ \leq\ z\ \leq\ 37$ ==>
x∈{35,36,37}
y∈{47,48,49}
z∈{141,144,147}

We must go futher:

if x=35 then y=4*35/3=46.666 not good , not whole
if x=36 then y=4*36/3=48 ok
if x=37 then y=37*4/3=49.333.. not good

So there is only one solution (36,48,144) for (x,y,z)

No problem with z for z=3/1*4/3*x=4x ==>whole.

7 0

3 years ago

You are trying to figure out how many gumballs you need to fill a 7.3 x 5.0 x 9.4 rectangular box for Halloween. Each gumball ha

riadik2000 [5.3K]

According to the calculations made, 410 gumballs will be needed to fill the box.

Since you are trying to figure out how many gumballs you need to fill a 7.3 x 5.0 x 9.4 rectangular box for Halloween, and each gumball has a radius of 1/2 in, if the packing density for spheres is 5/8 of the volume will be filled with gumballs while the rest will be air how many gumballs will be needed, to determine this amount the following calculation must be performed:

(Volume of box x 5/8) / volume of gumballs = Amount of gumballs
Volume of a sphere = 4/3 x 3.14 x (radius x radius x radius)
Volume of a gumball = 4/3 x 3.14 x (0.5 x 0.5 x 0.5) = 0.5235 inches
((7.3 x 5 x 9.4) x 5/8) / 0.523 = X
(343.1 x 5/8) / 0.523 = X
214.4375 / 0.523 = X
410 = X

Therefore, 410 gumballs will be needed to fill the box.

Learn more in brainly.com/question/1578538

4 0

3 years ago

Harriet used the work below to determine the percent equivalent to 1/8.

vampirchik [111]

Step 2 shows the error.

8 0

3 years ago

Read 2 more answers