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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I'm assuming you mean
Write the 2 as a fraction 2/1 and multiply.
Write the 2 as a fraction 2/1 and multiply.
Here are a couple I found:
<u>Similarities</u>:
- They have the same y-intercept of (0,5).
- They are both in slope-intercept form.
<u>Differences</u>:
- The line of y = -13x + 5 "falls" from left to right. The line of y = 2x + 5 "rises" from left to right.
- They have different x-intercepts. (y = 2x + 5 intersects (-
, 0) while y = -13x + 5 intersects at (
, 0)
<u></u>
<u>Explanation</u>:
Slope-intercept form is y = mx + b, and by looking at the equations, they both already fit that format, with m as their slope and b as their y-intercept. Also, since they both have a 5 as that "b," their y-intercepts are the same: (0,5).
As for differences, we can see that the coefficient in place of that "m" is positive in y = <u>2x</u> + 5 and negative in y = <u>-13x</u> + 5. Therefore, one line would rise due to their slope being positive and one would fall due to their slope being negative. They also have two different x-intercepts, which we can calculate by substituting 0 in place of the y, then isolating x.