Question
The graph of this system of equations is which of the following?
−2x + y = 3
4x + 2y = 2
−2x + y = 3
4x + 2y = 2
Answers
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One possible way to solve the system is to use the elimination method. Multiplying the first equation by 2 and subtracting it from the second equation, we get:
4x + 2y = 2
-(-4x + 2y = 6)
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8x = -4
Dividing both sides by 8, we obtain x = -1/2. Substituting this value into the first equation, we can solve for y:
-2x + y = 3
-2(-1/2) + y = 3
y = 4
Therefore, the solution to the system is (-1/2, 4), which represents the intersection of the two lines. To graph these lines, we could use their intercepts or slope-intercept forms.
For the first equation, when x = 0, y = 3, so the y-intercept is (0, 3). When y = 0, -2x + 0 = 3, so x = -3/(-2) = 3/2, and the x-intercept is (3/2, 0). We can plot these two points and draw a straight line passing through them.
For the second equation, when x = 0, 2y = 2, so the y-intercept is (0, 1). When y = 0, 4x + 0 = 2, so x = 1/2, and the x-intercept is (1/2, 0). We can plot these two points and draw a straight line passing through them.
The graph of the system is the point where these two lines intersect, which is approximately (-0.5, 4). This point is not shown in any of the given answer choices, so we cannot determine the correct answer without additional information.
4x + 2y = 2
-(-4x + 2y = 6)
------------------
8x = -4
Dividing both sides by 8, we obtain x = -1/2. Substituting this value into the first equation, we can solve for y:
-2x + y = 3
-2(-1/2) + y = 3
y = 4
Therefore, the solution to the system is (-1/2, 4), which represents the intersection of the two lines. To graph these lines, we could use their intercepts or slope-intercept forms.
For the first equation, when x = 0, y = 3, so the y-intercept is (0, 3). When y = 0, -2x + 0 = 3, so x = -3/(-2) = 3/2, and the x-intercept is (3/2, 0). We can plot these two points and draw a straight line passing through them.
For the second equation, when x = 0, 2y = 2, so the y-intercept is (0, 1). When y = 0, 4x + 0 = 2, so x = 1/2, and the x-intercept is (1/2, 0). We can plot these two points and draw a straight line passing through them.
The graph of the system is the point where these two lines intersect, which is approximately (-0.5, 4). This point is not shown in any of the given answer choices, so we cannot determine the correct answer without additional information.