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
PLEASE HELP FAST. EASY POINTS
MrRa [10]

To find the box to the top left, we can multiple the sides like rectangles. To find the top left box, we can multiply -1 and 0.5y to get -0.5y.

To find the box on the bottom right, we can multiply the sides like rectangles again. To find the bottom right box, we can multiply 24x and 3 to get 72x.

6 0
3 years ago
108 / (1/2) - 1 7/32? what is the answer to the following math problem?
Svet_ta [14]
214.78125. 108 / 1/2= 54 - 1 732= 214.78125
5 0
3 years ago
Explain how you would find the sum of 46+7.
Scorpion4ik [409]
Well you find the sum of 46+7 be adding it together and the answer is 53
6 0
3 years ago
Read 2 more answers
Lainey bought a set of 20 markers for 6$ . What is the cost of 1 marker
alukav5142 [94]

<em>Hope</em><em> </em><em>this</em><em> </em><em>w</em><em>i</em><em>l</em><em>l</em><em> </em><em>help</em><em> </em><em>u</em><em>.</em><em>.</em><em>.</em><em>.</em>

5 0
3 years ago
Read 2 more answers
A salesman earend a $325 salery this month. His total sales were $700. If the salesman earend a total of $360. What was his comm
Tatiana [17]

Answer:

Commission rate= 5% of sales

Step-by-step explanation:

Giving the following information:

Fixed salary= $325

Monthly salary= $360

Sales= $700

<u>First, we need to calculate the commissions:</u>

Commission= monthly salary  - fixed salary

Commission= 360 - 325

Commission= $35

<u>Now, the commission rate:</u>

Commission= commission rate* sales

35 = commission rate*700

0.05= commission rate

commission rate= 5% of sales

5 0
3 years ago
Other questions:
  • WHAT IS THE SURFACE AREA
    12·1 answer
  • Leo checks his pantry to see how much cat food he has. He finds a bag of Paw Picnic cat food with 3 cups left in it. Leo feeds h
    6·1 answer
  • Please help me with this question!
    15·1 answer
  • The GCF of 14 and 35 is _____.
    8·2 answers
  • For which function does f decrease by 15% every time x increases by 1
    14·1 answer
  • I need to know #21 and #22 in less than 30 min!!!
    15·2 answers
  • If the equation of the line is y=1/2x-3 find the x-coordinate of the point whose y coordinate is 5
    7·1 answer
  • You do mot have to exsplain the answer i just wat the correct answer<br> no links please
    12·1 answer
  • The volume of a cube is 1000 blocks. What is the length of one side of the cube?
    11·1 answer
  • Draw the image of the following triangle after a dilation centered at the origin with a scale factor of 2.
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!