Question

describe the substitution method and the elimination method of solving a system of equations. do they always give the same answers? what is the difference between the methods?

Answer 1

#part-1

substitution method:- in this method we solve one of the equations (you choose which one) for one of the variables (you choose which one), and then plugging this back into the other equation, "substituting" for the chosen variable and solving for the other. Then you back-solve for the first variable.

x+2y = 3 .....(1)

x+y = 1 .....(2)

by equation(2)

y = 1-x .....(3)

substitute the value of y in equation(1)

x+2(1-x) = 3

-x+2 = 3

x = -1 and y = 2

elimination method:-

In the elimination method you either add or subtract the equations to get an equation in one variable.When the coefficients of one variable are opposites you add the equations to eliminate a variable and when the coefficients of one variable are equal you subtract the equations to eliminate a variable.

x+2y = 3 .....(1)

x+y = 1 .....(2)

subtract equation (2) from equation(1) . we get

y = 2

now put this value of y into equation(2)

x = -1

#part-2

yes, both method give same answers always

#part-3

difference between methods can be understandble in #part-1 definition