1. Two lines, C and D, are represented by the following equations:
Line C: y = x + 5
Line D: y = −2x − 1
Which of the following options shows the solution to the system of equations and explains why?
(−2, 3), because the point does not lie on any axis
(−2, 3), because both lines pass through this point
(−2, 3), because one of the lines passes through this point
(−2, 3), because the point lies between the two axes****
Help Please Explain This!!
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Strange wording of the question.
Your choice of answer is incorrect.
Since the given point satisfies both equations, both lines must pass through the point (-2,3)
check:
http://www.wolframalpha.com/input/?i=plot+y+%3D+x+%2B+5+,+y+%3D+%E2%88%922x+%E2%88%92+1
To find the solution to the system of equations represented by Line C and Line D, we need to find the point of intersection of these two lines.
Line C has the equation: y = x + 5.
Line D has the equation: y = -2x - 1.
To find the point of intersection, we can set the two equations equal to each other and solve for x:
x + 5 = -2x - 1
Combining like terms, we have:
3x = -6
Dividing both sides by 3, we get:
x = -2
Now that we have the value of x, we can substitute it back into either equation to find the corresponding y-coordinate. Let's use Line C:
y = x + 5
y = -2 + 5
y = 3
Therefore, the point of intersection of Line C and Line D is (-2, 3).
Now, let's evaluate the given answer options:
- (−2, 3), because the point does not lie on any axis: This is incorrect, as the coordinates (-2, 3) do lie on the coordinate axes.
- (−2, 3), because both lines pass through this point: This is correct, as we found that (-2, 3) is the point of intersection of the two lines.
- (−2, 3), because one of the lines passes through this point: This is correct, Line C passes through the point (-2, 3).
- (−2, 3), because the point lies between the two axes: This is incorrect, as the point (-2, 3) does not necessarily lie "between" the coordinate axes.
Therefore, the correct answer is: (−2, 3), because one of the lines passes through this point.
To determine which option shows the solution to the system of equations, we need to analyze the given equations and their intersection point.
The two lines, C and D, are represented by the following equations:
Line C: y = x + 5
Line D: y = -2x - 1
To find the intersection point of these lines, we need to solve the system of equations by setting the y-values equal to each other:
x + 5 = -2x - 1
Now, we can solve for x:
3x = -6
x = -2
Substitute the value of x in one of the equations to find the y-coordinate:
y = -2(-2) - 1
y = 4 - 1
y = 3
Thus, the intersection point of these two lines is (-2, 3).
Now, let's analyze the given options:
(−2, 3), because the point does not lie on any axis: This option is incorrect because (-2, 3) lies on the x-axis.
(−2, 3), because both lines pass through this point: This option is correct, as both lines C and D pass through the point (-2, 3).
(−2, 3), because one of the lines passes through this point: This option is incorrect because both lines pass through the point (-2, 3), not just one.
(−2, 3), because the point lies between the two axes: This option is incorrect because (-2, 3) lies on the x-axis, not between the x and y axes.
Therefore, the correct option is (−2, 3), because both lines pass through this point.