1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Nezavi [6.7K]
1 year ago
13

Use Cramer Rule to solve the following system: 8x−5y=70 and 9x+7y=3

Mathematics
1 answer:
nlexa [21]1 year ago
7 0

Answer:

(x,y) = (5,-6)

Step-by-step explanation:

\underline{\textbf{Determinant of a matrix.}}\\\\\text{For a}~ 2 \times 2 ~ \text{matrix,}\\\\\begin{vmatrix} a_1&a_2\\b_1&b_2 \end{vmatrix} = a_1b_2 - a_2b_1\\\\\\\text{For a}~ 3 \times 3 ~ \text{matrix,}\\\\\begin{vmatrix} a_1&a_2&a_3\\ b_1&b_2&b_3\\ c_1&c_2&c_3 \end{vmatrix} = a_1\begin{vmatrix} b_2&b_3\\c_2&c_3 \end{vmatrix} - a_2 \begin{vmatrix} b_1&b_3\\c_1&c_3 \end{vmatrix}+ a_3 \begin{vmatrix} b_1&b_2\\c_1&c_2 \end{vmatrix}\\\\\\

                     ~~~~~~~~~~~~~~~~~~=a_1(b_2c_3-b_3c_2) -a_2(b_1c_3-b_3c_1) +a_3(b_1c_2-b_2c_1)

\underline{\textbf{Cramer's Rule to solve a system of two equations.}}\\\\\text{Consider the system of two equations:}\\\\~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~a_1x + b_1 y= c_1\\\\~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~a_2x +b_2 y = c_2\\\\\text{Here,}\\\\x = \dfrac{D_x}{D}= \dfrac{\begin{vmatrix} c_1&b_1\\c_2&b_2 \end{vmatrix}}{\begin{vmatrix} a_1&b_1\\a_2&b_2 \end{vmatrix}}\\\\\\ y= \dfrac{D_y}{D}= \dfrac{\begin{vmatrix} a_1&c_1\\a_2&c_2 \end{vmatrix}}{\begin{vmatrix} a_1&b_1\\a_2&b_2 \end{vmatrix}}\\\\

\underline{\textbf{Solution:}}\\\\~~~~~~~~~~~~~~~~~~~~~~~8x-5y = 70~~~~~~...(i)\\\\~~~~~~~~~~~~~~~~~~~~~~~9x +7y = 3~~~~~~~...(ii)\\\\\text{Applying Cramer's rule:}\\\\x = \dfrac{D_x}{D}\\\\\\~~=\dfrac{\begin{vmatrix} 70& -5 \\3&7 \end{vmatrix}}{\begin{vmatrix} 8& -5\\ 9& 7\end{vmatrix}}\\\\\\~~=\dfrac{70(7) -(-5)(3)}{(8)(7)-(-5)(9)}\\\\\\~~=\dfrac{490+15}{56+45}\\\\\\~~=\dfrac{505}{101}\\\\\\~~=5

y = \dfrac{D_y}{D}\\\\\\~~=\dfrac{\begin{vmatrix} 8& 70 \\9&3 \end{vmatrix}}{\begin{vmatrix} 8& -5\\ 9& 7\end{vmatrix}}\\\\\\~~=\dfrac{(8)(3) -(70)(9)}{(8)(7)-(-5)(9)}\\\\\\~~=\dfrac{24-630}{56+45}\\\\\\~~=-\dfrac{606}{101}\\\\\\~~=-6

\textbf{Hence, the solution to the system of equation is}~ (x,y) = (5,-6)

You might be interested in
Help me plzz show work plz​
iren2701 [21]

Answer:

B

Step-by-step explanation:

Use the formula for radius and circle circumference.

d=2r \\ \\ C=2\pi r

Since we know the diameter, if we divide that by 2, we can get the radius.

29.5/2=14.75

Now we can plug that value into the circumference formula to get the circumference.

C=2(14.75)\pi \\ \\ C=29.5\pi \\ \\ C=93

*Since we're rounding to the nearest inch.

7 0
3 years ago
Help me please !!! ASAP
jok3333 [9.3K]
When multiplying numbers a negative number will make a positive into a negative. Yet if multiplied again by another negative it will cancel out or make it positive again. Seeing as answer c has only one negative it's the correct answer.
4 0
3 years ago
Read 2 more answers
Identify the degree of the polynomial 8x^3y^2 – 10xy + 4x^2y^2 + 3.
Anastaziya [24]
When the polynomial has more than one variable you have to sum the exponents of the variables for every monomial. The largest sum is the order of the polynomial.

Here:

momomial   sum of the exponents
8x^3y^2       3 + 2  = 5
-10xy           1 + 1 = 2
4x^2y^2       2 + 2 = 4

Then the degree is 5.
3 0
3 years ago
Read 2 more answers
2 × √(7) + 5 × √(7) - √(7)
arsen [322]

Answer:

6√(7) is the simplified expression

Step-by-step explanation:

8 0
2 years ago
On a coordinate plane, point A is located at (7, 4), and point B is located at (-8, 4). What is the distance between the two poi
stiv31 [10]

Answer:

Step-by-step explanation:

Distance=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}\\\\ =\sqrt{(-8-7)^{2}+(4-4)^{2}}\\\\ =\sqrt{(-15)^{2}+0}\\\\=\sqrt{225} \\\\=15

5 0
3 years ago
Other questions:
  • Can someone please help me
    9·1 answer
  • Find h(6) if h(x) = x2 - 2x - 5.
    14·1 answer
  • If EFGH is a rectangle, what is FH?
    10·1 answer
  • Choose the correct sentence. choose one answer.
    9·1 answer
  • Geometry help plz will mark brainliest.
    12·1 answer
  • 4c+6+2<br><br> if anyone can tell me the answer it would mean so much!
    12·2 answers
  • Cuál es el valor de g(2.5)
    9·1 answer
  • Which facts could be applied to simplify this expression? Check all that apply.
    10·1 answer
  • A group of friends went out for dinner and decided to split the cost of the $196 bill equally. If each person contributed $30, t
    8·1 answer
  • If a trapezoid has an area of 21 cm and a height of 6cm, what are its bases?
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!