How many intersections are there of the graphs of the equations below?

One-halfx + 5y = 6

3x + 30y = 36

A. none
B. one
C. two
D. infinitely many

Question

How many intersections are there of the graphs of the equations below?

One-halfx + 5y = 6

3x + 30y = 36

A. none
B. one
C. two
D. infinitely many

darkknight · Answer

2 linear functions can never intersect twice, only 0 times, 1 time or infinitely many (if they overlap) so eliminate the second answer choice

darkknight · Answer

One-halfx + 5y = 6

3x + 30y = 36

1/2x + 5y = 6
3x+ 30y = 36
we can simplify the bottom equation by dividing both sides by 3
x+10y = 12
solving for y, we have 
10y = -x+12
(solve for y now)

For the first equation
1/2x+5y = 6
5y = -1/2x + 6
(solve for y now)

Can you solve for y in the above 2 equations and see what the equations simplify down too?

Lisaneedham · Answer

ok thanks