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The coordinates below represent two linear equations.


How many solutions does this system of equations have?


Line 1

x y

–3 6

3 4

Line 2

x y

–6 7

9 2



A.

0


B.

exactly 1


C.

exactly 2


D.

infinitely many

Verified Answer :

apologiabiology

the soluttion would be the interesctions of the lines

two line can only intercect in only 0 or one or all of the points (when the 2 lines are equal)

so the answers could be A,B, D

then we solve for the slope-intercept form

y=mx+b m=slope=(y1-y2)/(x1-x2)
and b=y intercept
line one
(6-4)/(-3-3)=2/-6=-1/3
y=-1/3x+b
subsitute -3 for x and 6 for y
6=-1/3(3)+b
6=-1+b
7=b

y=-1/3x+7 is the equation of the first line


second line(7-2)/(-6-(9))=5/-15=-1/3
y=-1/3x+b
subsitue -6 for x and 7 for y
7=-1/3(-6)+b
7=2+b
5=b
y=-1/3x+6

the equations are
y=-1/3x+7
y=-1/3x+6

since they have the same slope, they are parrelell, and since they do not have the same y-intercept, they are not on the same level

the do not intercect in any point

the answer is A, zero points/no solution

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