How many solutions does a system of two linear equations have if the slope of each equation is the same, but the y-intercepts are different? a. infinitely many b. none c. one d. none of the above

The correct answer is b. none

Step-by-step explanation:

The lines being described are parallel. Parallel lines have the same slope, but different y-intercepts. By definition, parallel lines do not intersect and therefore do not create a solution within a system.

B.) none

Step-by-step explanation:

In this case a solution means that these lines will intersect at some (x,y) point.  If the y-intercept is different but the slope is the same this means that the lines are never going to touch since they will be going up/down at the same rate.  This also means that both lines are parallel to one another, since the lines will never touch there will be no solutions.

{x = -1/2 ,   y = -1

step-by-step explanation:

solve the following system:

{2 x + y = -2

{10 x - 3 y = -2

in the first equation, look to solve for y:

{2 x + y = -2

{10 x - 3 y = -2

subtract 2 x from both sides:

{y = -2 x - 2

{10 x - 3 y = -2

substitute y = -2 x - 2 into the second equation:

{y = -2 x - 2

{10 x - 3 (-2 x - 2) = -2

10 x - 3 (-2 x - 2) = (6 x + 6) + 10 x = 16 x + 6:

{y = -2 x - 2

{16 x + 6 = -2

in the second equation, look to solve for x:

{y = -2 x - 2

{16 x + 6 = -2

subtract 6 from both sides:

{y = -2 x - 2

{16 x = -8

divide both sides by 16:

{y = -2 x - 2

{x = -1/2

substitute x = -1/2 into the first equation:

{y = -1

{x = -1/2

collect results in alphabetical order:

answer:   {x = -1/2 ,   y = -1

c. 6tan80

step-by-step explanation: