Provide a system of TWO equations in slope-intercept form, with only one solution. Using complete sentences, explain why this system has one solution.

Question

anonymous · Answer

Part 1: Provide a system of TWO equations in slope-intercept form, with only one solution. Using complete sentences, explain why this system has one solution.

Part 2: Provide a system of TWO equations in slope-intercept form with no solutions. Using complete sentences, explain why this system has no solutions.

Part 3: Provide a system of TWO equations in slope-intercept form with infinitely many solutions. Using complete sentences, explain why this system has infinitely many solutions.

anonymous · Answer

y = x +7
y = 2x +3
There is only one solution because (4,11) is the only point where two lines intersect.

anonymous · Answer

part 2 ?

anonymous · Answer

y = x + 7
y = x + 3
There is no solution because there is no point where the two lines intersect.

anonymous · Answer

And for part three, and equations that are the same have infinite solutions.

anonymous · Answer

how would you write that out because i need to explain each one

radar · Answer

While y= x + 7 and y = 2x + 3 has only one solution, i believe the intersection is 
at (4,3) rather than (4, 11)  Wouldn't you agree?

radar · Answer

The part 3, could use these:
y = x + 7
2y=2x + 14

They are identities and have infinite solutions.

anonymous · Answer

Part 1:
If you were solving a system of equations and you came to a statement like 1 = 3, what do you know about the solution(s) to this system? 

Part 2:
Solve the following system and show all of your work.
x − 2y = 14
x + 3y = 9  

HELP ME PLEASE.

radar · Answer

Part 1 The solution is not correct.
x = 2y + 14
x = -3y + 9       we know that x = x so we can write:
2y + 14 = -3y + 9
5y = -5
y = -1         substituting the -1 value into one of the original equation solving for x.
x = -2 +14
x=12