Mathematics 31 Online
OpenStudy (anonymous):

use the substitution method to solve the following system of equations. x+y=3 2x+2y=10

OpenStudy (anonymous):

no solution infinitely many solutions

OpenStudy (anonymous):

Niti to understand that there are no REAL solutions (There are of course an infinite number of imaginary solutions) multiply all in equation 1 by 2 giving x+y=3 is equal to 2x+2y=6 now if you subtract this equation from equation 2 you get... 2x+2y=10 - 2x+2y=6 showing that 0 = 4 which in real terms makes no sense and hence there are no real solutions to this particular problem.

OpenStudy (anonymous):

Niti to understand it graphically, you would see two parallel lines where one cuts the y axis at 3 and the other at 5. As the lines are parallel there can never be a popingt of intersection and hence they share no common coordinate point.

OpenStudy (anonymous):

Incorrect

OpenStudy (saifoo.khan):

my calc solvd it.

OpenStudy (saifoo.khan):

sorrrrrrry!

OpenStudy (anonymous):

You need a new calculator or you put something into it incorrectly

OpenStudy (saifoo.khan):

i wrote 2 instead of 1. :O

OpenStudy (anonymous):

Mistakes happen do not worry:)

OpenStudy (saifoo.khan):

:l

OpenStudy (anonymous):

actually it is very easy-step by step. 1. lets divide second part by two. 2x+2y=10/:2 we will get x+y=5 now we have set: x+y=3 x+y=5 now lets really try substitution. we will subtract second part from first part x+y-(x+y)=3-5 lets open the brackets: x+y-x-y=-2 0=-2 no solution) as 0 is not equal to -2

OpenStudy (anonymous):

i am not sure it is substitution method)) probably you had to express one variable in terms of other. then: x=3-y (first expression) now we plug it into 2-nd expression instead of x: 3-y+y=5 3=5 no solution

OpenStudy (anonymous):

taking the first equation,i.e.x+y=3,and dividing the second equtaion with 2,we'll get, x+y=5. comparing the two equations,we get the coefficients of the two variables in two equations are same.this satisfies the condition for parallel lines.as,parallel lines hav no solutions,the given two equations have no solutions.

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