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• Practice exercises 4.1a. sketch the graph of the f...

# Practice exercises 4.1a. sketch the graph of the following linear systems. then tell whether the system is indepen-dent, dependent or inconsistent.1) x + y = 5 x-y=32) x-y=-2 2x-2y=63) x+2y=6 -3x-6y=-64) x+y=1 2x-3y=85) x+3y=6 4x-y=46) 2x-y=6 -4x+2y=8 ​

• Réponse publiée par: Rosalesdhan

Step-by-step explanation:

This is how you determined the graph of two equalities.

First, be sure the same terms of equation 1 and equation 2 are on the same side.

for example:

x+ y =2

2x -3y= 4

This is good, because x and y on equation 1 and 2 are on the left side while both whole numbers on the right.

second, make a ratio of ax, by, and c for both equationnow if :ax:by:c has the same ratio from both equation the graph is consistent-dependent.ax:by has the same ratio but different c the graph is inconsistent.totaly different ratio is consistent-indepandent.

solve

let's see their ratios

1) x + y = 5 (1:1:5)

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

2) x-y=-2 (1 : -1 : -2 )

2x-2y=6 ( 2 : -2 : 6 ) or (1 : -1 : 3)

3) x+2y=6 (1 : 2 : 6)

-3x-6y=-6 (-3 : -6 : -6) or ( 1 : 2 : 2 )

4) x+y=1 ( 1 : 1 : 1 )

2x-3y=8 (2 : -3 : 8 )

5) x+3y=6 ( 1 : 3 : 6 )

4x-y=4 (4 : -1 : 4)

6) 2x-y=6 ( 2 : -1 : 6 )

-4x+2y=8 (-4 : 2 : 8 ) or ( 2 : -1 : -4 )

• Réponse publiée par: ian2145

Step-by-step explanation:

Graphs of linear system:

Independent:  The graphs intersect.

Different or unequal slopes (m)Different y-intercepts (b)If the product of slopes is -1, the graphs intersects and are also perpendicular to each other.

Dependent: The graphs overlap.

Same or equal slopes (m)Same y-intercepts (b)

Inconsistent: The graphs are parallel.

Same or equal slopes (m)Different y-intercepts (b)

Change each pair of equations to slope-intercept form ⇒ y=mx + b then identify the slopes (m) and y-intercepts (b):

1)  x + y = 5

y = -x + 5

x - y=3

y = x - 3

Slopes (m): -1 and 1

y- intercepts (b): 5 and -3

System: Independent

Graph: Intersects

2) x - y = -2

y = x + 2

2x - 2y = 6

2y/2 = 2x/2 -6/2

y = x - 3

Slopes (m):  1 (equal slopes)

y- intercepts (b): 2 and -3

System: Inconsistent

Graph: parallel

3) x + 2y = 6

2y/2 = -x/2 + 6/2

y = -x/2 + 3

-3x - 6y = -6

6y/6 = -3x/6 + 6/3

y = -x/2 +  2

Slopes (m):  -1/2 (equal slopes)

y- intercepts (b): 3 and 2

System: Inconsistent

Graph: parallel

4) x + y = 1

y = -x + 1

2x - 3y = 8

3y/3 = 2x/3 - 8/3

y = 2x/3 - 8/3

Slopes (m):  -1 and 2/3

y- intercepts (b): 1 and -8/3

System: Independent

Graph: Intersects

5) x + 3y = 6

3y/3 = -x/3 + 6/3

y = -x/3 + 2

4x - y = 4

y = 4x - 4

Slopes (m):  -1/3 and 4

y- intercepts (b): 2 and -4

System: Independent

Graph: Intersects

6) 2x - y = 6

y = 2x - 6

-4x + 2y = 8

2y/2 = 4x/2 + 8/2

y = 2x + 4

Slopes (m):  2 (equal slopes)

y- intercepts (b): -6 and 4

System: Inconsistent

Graph: Parallel

(Please click the image below and enlarge to view the graphs.)

• Réponse publiée par: meteor13

a. falls to the left, rises to the right

b.rises to the left, falls to the right

c. falls to the left, rises to the right

Step-by-step explanation:

If the leading coefficient is positive ( greater than zero ), then the graph falls to the left and rises to the right. If the leading coefficient is negative ( less than zero ), then the graph rises to the left and falls to the right.