A system of linear equations is graphed. Which ordered pair is the best estimate for the solution to the system? (12, 0) (1, 1)
(12, 1) (13, 0) A system of 2 linear equations graphed on a coordinate plane. The horizontal x-axis ranges from negative 5 to 5 in increments of 1. The vertical y-axis ranges from negative 5 to 5 in increments of 1. First line passes through begin ordered pair 0 comma 2 end ordered pair and begin ordered pair 1 comma negative 1 end ordered pair. Second line passes through begin ordered pair 0 comma negative 1 end ordered pair and begin ordered pair 2 comma 2 end ordered pair.
2 answers:
Line 1--------- >(0,2) (1,-1)
y=mx+b m=(-1-2)/(1-0)=-3
2=(-3)*(0)+b----- > b=2
y1=-3x+2
Line 2--------- >(0,-1) (2,2)
y=mx+b m=(2+1)/(2-0)=3/2
-1=(3/2)*(0)+b----- > b=-1
y2=(3/2)x-1
<span>using a graphic tool
see attached figure</span>
the best estimate solution for the system is <span>(1, 1)
because </span>is the only one within the range of the x axis (-5,5) and the y axis (-5,5)
y=mx+b m=(-1-2)/(1-0)=-3
2=(-3)*(0)+b----- > b=2
y1=-3x+2
Line 2--------- >(0,-1) (2,2)
y=mx+b m=(2+1)/(2-0)=3/2
-1=(3/2)*(0)+b----- > b=-1
y2=(3/2)x-1
<span>using a graphic tool
see attached figure</span>
the best estimate solution for the system is <span>(1, 1)
because </span>is the only one within the range of the x axis (-5,5) and the y axis (-5,5)
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<h3>Answer: Choice C</h3>
{x | x < -12 or x > -6}
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Explanation:
Let's solve the first inequality for x.
(-2/3)x > 8
-2x > 8*3
-2x > 24
x < 24/(-2)
x < -12
The inequality sign flips when we divide both sides by a negative value.
Let's do the same for the second inequality.
(-2/3)x < 4
-2x < 4*3
-2x < 12
x > 12/(-2)
x > -6
The conclusion of each section is that x < -12 or x > -6 which points us to <u>choice C</u> as the final answer.
Side note: The intervals x < -12 and x > -6 do not overlap in any way. There's a gap between the two pieces. We consider these intervals to be disjoint. The number line graph is below.