Two lines, R and M, are represented by the following equations:
2 answers:
Answer: The correct option is (C) infinitely many solutions.
Step-by-step explanation: The representations of two lines 'R' and 'M' are given by
We are to select the TRUE statement about the solution to the above set of equations.
Multiplying equation (ii) by 2, we have
From equations (i) and (iii), we can conclude that
the equations for line 'R' and line 'M' are same, and hence their graph is the same straight line as shown in the attached figure.
Therefore, each point on the lines is a solution to the given system, because both the lines intersect at each and every point that lies on the lines.
For example, (0, 9), (9, 0), (4, 5), etc. are solutions to the system.
Thus, there are infinitely many solutions.
Option (C) is correct.
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Since you haven't provided the graph, I'll explain each one and you choose the one suiting your given.
<u>The parent modulus function is:</u>
g(x) = |x|
It is centered at the origin and opens upwards.
A coefficient inside the modulus |x+k| means that the function is shifted along the x-axis
If "k" is <u>positive</u>, the shift will be to the <u>left</u>. If "k" is <u>negative</u>, the shift will be to the <u>right</u>.
A coefficient outside the modulus |x| + h means that the function is shifted along the y-axis
If "h" is <u>positive</u>, the shift will be <u>upwards</u>. If "h" is <u>negative,</u> the shift will be <u>downwards</u>.
<u>Now, let's check each of the options:</u>
<u>g(x) = |x+4| - 2 :</u>
This function is shifted 4 units to the left and 2 units down. It will be centered at (-4,-2). Check the blue graph in the attachment.
<u>g(x) = |x-4| - 2 :</u>
This function is shifted 4 units to the right and 2 units down. It will be centered at (4,-2). Check the black graph in the attachment.
<u>g(x) = |x-2| - 4 :</u>
This function is shifted 2 units to the right and 4 units down. It will be centered at (2,-4). Check the red graph in the attachment.
<u>g(x) = |x-2| + 4 :</u>
This function is shifted 2 units to the right and 4 units up. It will be centered at (2,4). Check the green graph in the attachment.
All 4 graphs are shown in the attached picture.
Hope this helps :)
