Question

Which equation shows the substitution method being used to solve the system of linear equations?



x + y = 6
x = y + 5




A.


(y + 5) + y = 6


B.


x + (y + 5) = 6


C.


x + y = y + 5


D.


x = (x – 6) + 5

Answer 1

The second equation is solved for x already, put y+5 into the first equation where you see the x,

Answer 2

x + y = 6

x = y + 5

Answer 3

exactly ^^ just sub in y + 5 in for x back into the 1st equation

Answer 4

its A

Answer 5

yea

Answer 6

im pretty sure it is

Answer 7

good job :)

Answer 8

can you guys help me with another one?

Answer 9

If one wasnt already solved for a variable, like x = y + 5

you would have to do an extra step and solve for a variable in one of the equations first

Answer 10

sure post er up

Answer 11

For example, this is the same question here

x + y = 6
x - y = 5

But you have to isolate a variable first, they already did that for you.

x + y = 6
x = 5 + y

Answer 12

The system of equations is inconsistent.



What are the missing values?

5x+_y=2 _x+3y=8

Answer 13

Inconsistent means there are no solutions, where the two lines intersect. They are parallel lines.

5x + _y = 2
_x + 3y = 8

When 2 lines are parallel, the coefficients in front of the X and the Y in those 2 equations will be a multiple of one another.

Answer 14

Mhm

Answer 15

if you say the first one is

5x + 1y = 2
_x + 3y = 8

if you let the first equation have a 1 on the Y variable, you can see moving to the second equation, the 3y, is 3 times the first equations y

Answer 16

The second equation will be 3 times the first on the x and y variables if you let the first equations y be 1.

so the x variable in the second equation will be 3 times the 5x, which is 15x

Answer 17

5x + 1y = 2
15x + 3y = 8

Now the second equations left side is 3 times the first

Answer 18

then what about the other value

Answer 19

the right side?

Answer 20

ya

Answer 21

Parallel lines, Inconsistent, zero solutions
5x + 1y = 2
15x + 3y = 8

If the right side was also the same multiple of 3 like the left side is, for example

5x + 1y = 2
15x + 3y = 6

The lines are the same exact line, you can divide the second equation by 3 and get the first back again. Here there are infinite solutions, dependent, overlapping lines

Answer 22

mhm

Answer 23

this might help out some.
http://www.algebra.com/algebra/homework/coordinate/Types-of-systems-inconsistent-dependent-independent.lesson

Answer 24

k let me see

Answer 25

For example if you have...

x + y = 1
2x + 2y = 2

those are the same line

Answer 26

if you have

x + y = 1
2x + 2y = 34

those are parallel lines, the left is multiplied by 2, but the right is different than that.

Answer 27

is it 10?

Answer 28

what do you mean?

Answer 29

the solution left

Answer 30

10y?