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
Dominik [7]
3 years ago
13

Ax+by=(a-b) , bx - ay =(a+b) simultaneous linear equations using cross multiplication

Mathematics
1 answer:
Molodets [167]3 years ago
6 0

Answer:

x=1\,,\,y=-1

Step-by-step explanation:

Given: ax+by=a-b\,,\,bx-ay=a+b

To solve: the given linear equations

Solution:

Consider the equations:

A_1x+B_1y+C_1=0\\A_2x+B_2y+C_2=0

By method of cross multiplication:

\frac{x}{B_1C_2-B_2C_1}=\frac{y}{C_1A_2-C_2A_1}=\frac{1}{A_1B_2-A_2B_1}

For equations: ax+by=a-b\,,\,bx-ay=a+b

ax+by-(a-b)=0\\bx-ay-(a+b)=0

Take A_1=a\,,\,B_1=b\,,\,C_1=-(a-b)\,,\,A_2=b\,,\,B_2=-a\,,\,C_2=-(a+b)

So,

\frac{x}{-b(a+b)-a(a-b)}=\frac{y}{-b(a-b)+a(a+b)}=\frac{1}{-a^2-b^2}\\\frac{x}{-ab-b^2-a^2+ab}=\frac{y}{-ab+b^2+a^2+ab}=\frac{1}{-(a^2+b^2)}\\\frac{x}{-(a^2+b^2)}=\frac{y}{a^2+b^2}=\frac{1}{-(a^2+b^2)}\\\frac{x}{-(a^2+b^2)}=\frac{1}{-(a^2+b^2)}\,,\,\frac{y}{a^2+b^2}=\frac{1}{-(a^2+b^2)}\\x=1\,,\,y=-1

You might be interested in
An angle measures 51.4° less than the measure of its complementary angle. What is the measure of each angle?
kap26 [50]

Answer:

70.7 deg, 19.3 deg

Step-by-step explanation:

The sum of the measures of complementary angles is 90 deg.

One angle measures x.

The other angles measures 51.4 deg less than x, or x - 51.4.

The sum of their measures equals 90.

x + x - 51.4 = 90

2x - 51.4 = 90

2x = 141.4

x = 70.7

x - 51.4 = 70.7 - 51.4 = 19.3

Answer: 70.7 deg, 19.3 deg

5 0
3 years ago
What is x equal to if y = x / y.
kupik [55]

Answer: X= y^2

Step-by-step explanation:

7 0
3 years ago
Please help
tankabanditka [31]

Answer: (2a+2b,2c)

the first one

Step-by-step explanation:

you can add or subtract letter such as *a or *b so you "add" them which is 2a+2b and "y" for point B is 2c so it stays the same

sorry i such at explaining

4 0
4 years ago
A _____ tessellation is a tessellation that uses only one regular polygon to cover a surface completely.
matrenka [14]

Answer:

Regular

Step-by-step explanation:

The answer to this question is a regular tessellation. A regular tessellation can be explained as a cover design of the plane which is done by making use of 1 type of regular polygon.

In order To make a regular tessellation, we have to make sure that the internal angle of the polygon can divide 360. This way there won't be gaps.

6 0
3 years ago
Help please omg lord
ludmilkaskok [199]

Answer:

"Not really sure sorry"

Step-by-step explanation:

7 0
3 years ago
Other questions:
  • I know this isn't math but what would be the topic sentence? "First of all, being alive and healthy is key to a persons happines
    7·1 answer
  • Solve the system by substitution 5x+3y=8 3x+y=8
    9·1 answer
  • Name each of the following lines, line segments, and rays.
    12·2 answers
  • The local radio station is giving away some tickets to the circus. Adult tickets cost $8 each and children's ticket cost $6 each
    8·1 answer
  • Calculating conditional probability
    5·1 answer
  • Help please asap !! it doesn’t hurt to guess also! Thanks
    13·2 answers
  • 2 Fred and Ted each have a savings account. Fred's savings account is represented in the table below.
    5·1 answer
  • Rationalise the denominator by 6 root 7 minus 1
    12·1 answer
  • Khan academy distance formmula
    12·1 answer
  • A blueprint of a building has a scale of 3/4 inch = 10 feet. The actual height of the building is 48 feet. Determine the height
    12·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!