X - y= 4 , 2x + y= 5 solve linear equations and express in ordered pairs?

Question

Is system independent, inconsistent or dependent? Please show algebraic steps used to get this answer.

Answer 1

Best Answer - Chosen by Asker

To find the ordered pair, you use either substitution or you can combine the equations. I think substitution's more fun, so I'll do that.

x-y=4 -> y=x-4
2x+y=5 -> 2x+x-4=5 -> 3x=9 -> x=3
y=x-4 -> y=3-4 -> y=-1

The ordered pair is, therefore, (3,-1). You can check this if you want by plugging the numbers back into the original equations.

Because the lines for y=x-4 and y=5-2x are not parallel and intersect at one point, the system is independent.

Source(s):

http://www.purplemath.com/modules/systli…

Asker's Rating:

Asker's Comment:

Simplistic breakdown- great teaching mechanism!

Answer 2

x - y = 4 (EQ1)
2x + y = 5 (EQ2)

Solve EQ1 for x:
x = y + 4

Substitute this value into EQ2:
2(y + 4) + y = 5

Solve for y:
2y + 8 + y = 5

3y = -3

y = -1

Plug into EQ1 and solve for x:
x - (-1) = 4

x + 1 = 4

x = 3

Solution:
(3, -1)
Dependent

Answer 3

x - y = 4
2x + y = 5
¯¯¯¯¯¯¯¯¯¯¯
- x = - 1 (Subtract second equation from first)
x = 1

1 - y = 4 (Substitute 1 for y)
- y = 4 - 1
- y = 3
y = - 3

Ordered Pair (1, - 3)
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

Answer 4

x=3 y= -1

independent

1x - 1y = 4
2x + 1y = 5
-------------------
3x + 0y = 9

x = 3
y=-1

Answer 5

x=3 y= -1

independent

1x - 1y = 4
2x + 1y = 5
-------------------
3x + 0y = 9

x = 3
y=-1

Answer 6

when x-y=4
And 2x+y=5

x=4+y
then 2( 4+y ) + y=5
8+2y+y=5 & 3y=5-8 then 3y=-3
Y = -1
x - ( -1 ) =4 & x+1=4
X = 3

Answer 7

2x+y=5 ; x-y=4
2(3)+(-1)=5 (3)-(-1)=4
6-1=5 3+1=4

x=3 ; y= -1

not sure. XD

Source(s):

http://www.algebra.com/algebra/homework/coordinate/lessons/Types-of-systems-inconsistent-dependent-independent.lesson