Answer:
The system is inconsistent because there is no solution.
Step-by-step explanation:
I'm going to put both of these in slope-intercept form (y=mx+b where m is slope and b is y-intercept).
3x-6y=20
Solve for y.
3x-6y=20
Subtract 3x on both sides:
-6y=-3x+20
Divide both sides by -6:
y=(-3/-6)x+(20/-6)
Reduce:
y=(1/2)x+(-10/3)
The slope is 1/2 and the y-intercept is -10/3.
2x-4y=3
Solve for y.
2x-4y=3
Subtract 2x on both sides:
-4y=-2x+3
Divide both sides by -4:
y=(-2/-4)x+(3/-4)
Reduce:
y=(1/2)x+(-3/4)
The slope is 1/2 and the y-intercept is -3/4.
The lines are parallel so they have no intersection. I know they are parallel because they have the same slope and different y-intercept.
The system is inconsistent because there is no solution.
Answer:
B) Inconsistent
Step-by-step explanation:
Step 1: Write both equations
3x - 6y = 20
2x - 4y = 3
Step 2: Find x in terms of y
3x - 6y = 20
x = 20+6y/3
Step 3: Substitute x in one of the equations to find y
2x - 4y = 3
2(20+6y/3) - 5y = 3
40 + 12y - 12y = 9
0 ≠ -31
Therefore, these system of equations have no solution.
Step 4: Choose the option
A) consistent- A consistent system of equations has at least one set of equations. Therefore, this option is incorrect.
B) inconsistent- An inconsistent system of equations has no solution. Therefore, this option is correct.
C) Independent- An independent system of equations has one solution. Therefore, this option is incorrect.
D) Dependent- A dependent system of equations have infinite solutions. Therefore, this option is incorrect.
Option B is the right answer
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