Question

Choose the correct equation type for each system. (Equivalent, Inconsistent, Consistent)

Answer 1

Inconsistent
Equivalent
Inconsistent
Consistent
Consistent
Equivalent

Answer 2

Solution:

Equivalent= When two lines are coincident , they are said to be Equivalent.

Inconsistent= When two lines are parallel , they are said to be Inconsistent.

Consistent=  When two lines are intersecting, they are said to be consistent.

1. {(y=3x-2),(3x-y+4):}

y=3x-2, y = 3x +4

Both lines have same slope, i.e 3 , they are parallel.(Inconsistent)

2. {((1)/(2)y=-x+5),(2y=-4x+20):}

y = -2 x +10, y = - 2 x + 10

Both lines have same slope, i.e (-2) , they are Coincident.(Equivalent)

3. {(y=-x+4),(x=-y-6):}

y= -x + 4, y = -x -6

Both lines have same slope, i.e (-1) , they are parallel.(Inconsistent)

4. {(y=4x+2),(y=6x-10):}

Both lines have different slope.They are intersecting lines.(Consistent)

5. {(y=2x+1),(y=-2x+3):}

Both lines have different slope.They are intersecting lines.(Consistent)

6. {(-2x+5y=0),(y=(2)/(5)x):}

y=$\frac{2x}{5}$, y=$\frac{2x}{5}$

Both lines have same slope, i.e ($\frac{2x}{5}$) , they are parallel.(Inconsistent)