Using these axioms : commutativity, associativity,, distributivity, the additive identity, multiplicative identity, additive inverse, cancellation and replacement property.

prove the following statement

if a, b et and a +b=0 then, b= -a.

See explanation below

Step-by-step explanation:

a + b = 0

The additive identity establishes that if you add a real number to zero, then you get the same real number back.

The additive inverse of a number x is -x (because x + (-x) = 0)

a+b = 0, but by the additive identity we can add -a (the additive inverse of a) to both sides of the equation:

a + b - a = 0 - a

a + b - a = -a (Now, using the Cancellation property we can cancel a and -a on the left side)

b = -a

none.

step-by-step explanation:

m

1

=

5

m1=5

b

=

−

1

b=-1

find the slope and y-intercept of the second equation.

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m

2

=

0

m2=0

b

=

−

6

b=-6

compare the slopes

m

m of the two equations.

m

1

=

5

,

m

2

=

0

m1=5,m2=0

compare the two slopes in the decimal form. if the slopes are equal, then the lines are parallel. if the slopes are not equal, then the lines are not parallel.

m

1

=

5

,

m

2

=

0

m1=5,m2=0