Question

I need help solving these with different methods.

A. 3x-9y=3
6x-3y=-24 I need to put this one into elimination.

B. 7x-3y=20
5x+3y=16 I need this one in Substitution.

C. y=1/2x-6
2x+6y=19 I need this one in Elimination.

An explanation would be greatly appreciated Thanks!

Answer 1

A. 3x - 9y = 3 reduces to x - 3y = 1
6x - 3y = -24 reduces to 2x - y = - 8
so now we have :
x - 3y = 1-->(-2)
2x - y = -8
-------------
-2x + 6y = -2 (result of multiplying by -2)
2x - y = -8
-------------add
5y = -10
y = -2
now sub -2 in for y in either of original equations
x - 3y = 1
x -3(-2) = 1
x + 6 = 1
x = 1 - 6
x = -5
check..
2x - y = -8
2(-5) - (-2) = -8
-10 + 2 = -8
-8 = -8 (correct)
x = -5 and y = -2

Do you have any questions about this one ?

Answer 2

The only question is why did you reduce at the beginning of the problem?

Answer 3

it is not necessary to reduce...it can still be solved without reducing. I just have a habit of reducing to make things easier to solve.

Answer 4

Ok, Can you help me with the 2nd and 3rd one as well?

Answer 5

7x + 3y = 20
7x = -3y + 20
x = -3/7y + 20/7

now sub -3/7y + 20/7 in for x in the other equation
5x + 3y = 16
5(-3/7y + 20/7) + 3y = 16 -- distribute through the parenthesis
-15/7y + 100/7 + 3y = 16 -- multiply the entire equation by 7
-15y + 100 + 21y = 112 -- subtract 100 from both sides
-15y + 21y = 112 - 100 -- combine like terms
7y = 12
y = 12/7
now sub 12/7 in for y in either equation to find x
7x + 3y = 20
7x + 3(12/7) = 20
7x + 36/7 = 20 -- multiply by 7
49x + 36 = 140 -- subtract 36 from both sides
49x = 140 - 36
49x = 104
x = 104/49
check...
7x + 3y = 20
7(104/49) + 3(12/7) = 20
728/49 + 36/7 = 20
728/49 + 252/49 = 20
980/49 = 20
20 = 20 (correct)

x = 104/49
y = 12/7

any questions ?

Answer 6

There are times when I multiplied the entire equation by the LCD...I did this to get rid of the fractions and turn them to whole numbers

Answer 7

I would help you with the last one, but I have to go somewhere...I am sorry. I will be back on later if you need more help :) Again, I am sorry

Answer 8

Alright Thank you for your help. Your a lifesaver! :D