Question

3. How many solutions does the system of equations have?

4x = -12y + 16 and x + 3y = 4

a.) one
b.) two
c.) infinitely many
d.) none

4.) How many solutions does the system of equations have?

y = 6x + 2 and y = 6x + 4

a.) one
b.) two
c.) infinite
d.) none

Answer 1

3. c) infinitely many

4. d) none

Explanation:

3.

Rewriting the first equation by dividing by 4 and adding 3y gives ...

4x = -12y +16 . . . . .given

x = -3y +4 . . . . . . . divide by 4

x +3y = 4 . . . . . . . . add 3y

This is identical to the second equation, so both equations describe the same line. Each of the points on one line is also a point on the other line, so they intersect in an infinite number of places.

There are infinitely many solutions.

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4.

If you subtract the first equation from the second, you get ...

(y) -(y) = (6x +4) -(6x +2)

0 = 2

This is always false. There are no values of the variables that will make this true.

There are no solutions.