Question

Which equation is a linear equation?

a)

2/3xy − 3/4y = 0

b)

3a + 5b = 3


c)

4m2 = 6


d)

x2+y2 = 0

Answer 1

For this case we have that by definition, a linear equation is of the form:

`y = mx + b`

Thus, we have the following options:

Option A:

`\frac {2} {3xy} - \frac {3} {4y} = 0`

It is not a linear equation !!

Option B:

`3a + 5b = 3\\5b = 3-3a\\b = - \frac {3} {5} a + \frac {3} {5}`

It is a linear equation!

Option C:

`4m ^ 2 = 6`

It is a quadratic equation, the exponent of the variable is 2.

Option D:

`x ^ 2 + y ^ 2 = 0`

It is a quadratic equation, the exponents are quadratic!

Answer:

Option B

Answer 2

b) 3a + 5b = 3

Explanation:

An equation is linear if each term is a constant or is of degree 1, that is, it has only one variable to the first power.

__

a) the term containing xy is 2nd-degree

b) all non-constant terms are 1st-degree -- this is a linear equation

c) m^2 is a 2nd-degree term

d) x^2 and y^2 are both 2nd-degree terms