Use the substitution method to solve the system of equations. Choose the correct ordered pair. 2x-y=8 y=x-3
2 answers:
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<h3>Answer: No, it is not a solution</h3>
Explanation:
Refer to the diagram below. The point (-4,3) marked in red is outside the blue shaded region. So it doesn't make both inequalities true, and therefore not considered a solution.
In contrast, a point like (-5,1) is a solution as it is in the shaded region.
Put another way, the set of all solution points must be below both the solid line and the dashed line. Points can be on the solid line, but must be adjacent to the blue shaded region. The fact (-4,3) is on the solid line doesn't count because its not below the dashed line.
I don't know if we can find the foci of this ellipse, but we can find the centre and the vertices. First of all, let us state the standard equation of an ellipse.
(If there is a way to solve for the foci of this ellipse, please let me know! I am learning this stuff currently.)
Where
is the centre of the ellipse. Just by looking at your equation right away, we can tell that the centre of the ellipse is:
Now to find the vertices, we must first remember that the vertices of an ellipse are on the major axis.
The major axis in this case is that of the y-axis. In other words,
So we know that b=5 from your equation given. The vertices are 5 away from the centre, so we find that the vertices of your ellipse are:
&
I really hope this helped you! (Partially because I spent a lot of time on this lol)
Sincerely,
~Cam943, Junior Moderator
(If there is a way to solve for the foci of this ellipse, please let me know! I am learning this stuff currently.)
Where
Now to find the vertices, we must first remember that the vertices of an ellipse are on the major axis.
The major axis in this case is that of the y-axis. In other words,
So we know that b=5 from your equation given. The vertices are 5 away from the centre, so we find that the vertices of your ellipse are:
&
I really hope this helped you! (Partially because I spent a lot of time on this lol)
Sincerely,
~Cam943, Junior Moderator