Question

how do u solve
4x+5y=7
7y-x=23

Answer 1

u can solve it by substitution method
or by elimination method
or by cross-multiplication method....

choice is yours ☺

Answer 2

well can u show me any chice lets say elimatnion

Answer 3

multiply bottom equation by 4 you will do this so that it you can eliminate the x variable when adding both equations so you will be left with only one equation on the y variable
4x-4x+5y+28y=7+92 and that is 33y=99 and you should be able to solve that one and then replace the result on any of the other original equations to get the value for x

Answer 4

4x + 5y = 7
7y - x = 23

Take the first equation and solve for x in terms of y:
4x + 5y = 7
4x = 7 - 5y
x = (7 - 5y)/4

Now plug this value of x into the other equation:
7y - x = 23
7y - ((7 - 5y)/4) = 23

Solve for y:
7y * (4/4) - ((7 - 5y)/4) = 23
28y/4 - (7 - 5y)/4 = 23
(28y - 7 + 5y)/4 = 23
28y - 7 + 5y = 92
33y - 7 = 92
33y = 99
y = 3

plug y into one of the equations to solve for x:
4x + 5y = 7
4x + 5(3) = 7
4x = -8
x = -2

Answer 5

@harkirat
what is the cross-multiplication method?

Answer 6

wait i'll come back to reply....

Answer 7

if u have a system of linear equations in two variables x and y as follows:

a1x + b1y + c1 = 0 and
a2x + b2y + c2 = 0

then
x y 1
------------ = -------------- = --------------
b1c2-b2c1 c1a2 - c2a1 a1b2 - a2b1

Answer 8

ok thanks, i see how that works just never seen that method used before

Answer 9

thnaks

Answer 10

its basically cramers rule when using matrices

Answer 11

thats usually too advanced for h.s algebra students

Answer 12

to remember this easily we write the coefficients and variables as shown in the attached file (and you will see why we call it cross-multiplication method

Answer 13

In India, I never heard of Cramer's rule !!!

We just teach it as cross-multiplication method.....

Answer 14

o ok...yeah sorry US here obviously education curriculum is different

Answer 15

yeah some "cultural" differences....
I see you people using many shortcuts and calculators etc for many question, which we never do in India...

Answer 16

In school we have to do everything with full/proper method. However, in competitive exams, u can use shortcuts for calculations ☺

Answer 17

4x + 5y = 7 7y - x = 23 Take the first equation and solve for x in terms of y: 4x + 5y = 7 4x = 7 - 5y x = (7 - 5y)/4 Now plug this value of x into the other equation: 7y - x = 23 7y - ((7 - 5y)/4) = 23 Solve for y: 7y * (4/4) - ((7 - 5y)/4) = 23 28y/4 - (7 - 5y)/4 = 23 (28y - 7 + 5y)/4 = 23 28y - 7 + 5y = 92 33y - 7 = 92 33y = 99 y = 3 plug y into one of the equations to solve for x: 4x + 5y = 7 4x + 5(3) = 7 4x = -8 x = -2

Answer 18

ideally we aim to do the same, however, there are many standards that have to taught and there are now much more standardized tests for students so teachers just give them the shortcuts

Answer 19

http://en.wikipedia.org/wiki/Cramers_rule

Answer 20

Well, I find the Indian schooling system being modified and I do not like it at all.
In my time if one scored 70% marks, one was considered a brilliant student. At that time the all-India topper used to score about 85% marks.

Nowadays students r scoring 90% plus marks and not getting admission in colleges because the percentage of students scoring 90% plus marks has increased like plague.....

Answer 21

thanks for the link.. :))