Question

Solve the following system by substitution.
7x + 2y = 16
–21x – 6y = 24

Please show me step by step how to do this. I used to be pretty good at working with Systems of Equations but I seem to have forgotten how to work this out because I am SO confused.

Answer 1

you want to try to get a variable by itself so you can sub it back into the other equation.
If you can reduce an equation, do so...

for instance , -21x - 6y = 24....divide everything by 3 and you get : -7x - 2y = 8

now we have :
-7x - 2y = 8 -- add 2y to both sides
-7x = 2y + 8 -- divide by -7
x = -2/7y - 8/7

now sub -2/7y - 8/7 in for x in the other equation
7x + 2y = 16
7(-2/7y - 8/7) + 2y = 16 -- distribute through the parenthesis
-2y - 8 + 2y = 16 -- add 8 to both sides
-2y + 2y = 16 + 8
0 = 24 (incorrect)

there is no solution to this.

Answer 2

it is not necessary to reduce the equations...it just makes it easier because you are dealing with smaller numbers

do you understand what I did ? Do you have any questions ?

Answer 3

So when I sub for the variable in the other equation, I'm using the whole new equation for x/y ?

Answer 4

um...I do not understand you question.

Lets say you have these equations..
x + 3y = 5 ----> x = -3y + 5
2x + 4y = 7

now you would sub -3y + 5 in for x in the other equation...like this
2(-3y + 5) + 4y = 7

does that make sense to you ?

Answer 5

let me do it without reducing....
7x + 2y = 16
2y = -7x + 16
y = -7/2x + 8
now sub -7/2x + 8 in for y in the other equation
-21x - 6y = 24
-21x - 6(-7/2x + 8) = 24
-21x + 21x - 48 = 24
-21x + 21x = 24 + 48
-21x + 21x = 72
0 = 72 (incorrect)
NO SOLUTION

Answer 6

You answered my questions.
Thank you very much; I think I understand. ♥

Answer 7

good to hear :)