Question 181687: a) An infinite number of ordered pairs, including (0,1) (1,0) and (2,-1) satisfis both equations. Explain why.
x+y=1
y=2x+3
b) no ordered pair satisfies both equations. Expain why
y=2x+1
y=2x+3
thankyou
Answer by Mathtut(3670)   (Show Source):
You can put this solution on YOUR website! a) An infinite number of ordered pairs, including (0,1) (1,0) and (2,-1) satisfis both equations. Explain why.
x+y=1
y=2x+3
b) no ordered pair satisfies both equations. Expain why
y=2x+1
y=2x+3
:
a)
x+y=1.....eq 1
y=2x+3....eq 2......lets re write these
:
y=-x+1....eq 1
y=2x+3....eq 2
: either they have a typo or you made a typo.....this system of equation has only one solution.
:
take y's value from eq 1 and plug it into eq 2
:
-x+1=2x+3
:
-3x=2
:
x=-2/3
:
y=-(-2/3)+1
:
y=5/3
:
solution is (-2/3,5/3)
:
the only way a system can have infinite solutions is if one line is the same line as the other. In other words the 2 lines are multiples of each other such as 2x+3y=3 and 6x+9y+9......the 2nd being 3 times more than the first. This is what we would call a consistent and dependent system
:
b)b) no ordered pair satisfies both equations. Expain why
y=2x+1
y=2x+3
:the reason there is NO solution here is these lines are parallel(NO intersection) This is what we call an inconsistent system
:
the way we can tell that is they have the same slope(2) and yet have different y intercepts
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