The graph of this system of equations is which of the following?
−2x + y = 3
4x + 2y = 2
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.
To determine the graph of the system of equations, we need to graph each equation separately and see where they intersect.
Let's start by graphing the first equation: -2x + y = 3.
To graph this equation, we can rearrange it into slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept.
-2x + y = 3
y = 2x + 3
Now we can plot the graph of this equation:
Plot the y-intercept (0, 3).
Use the slope of 2 to find another point. For example, if we move 1 unit to the right (x = 1), we move 2 units upward (y = 5). Plot this point.
Draw a straight line through these two points.
Now let's graph the second equation: 4x + 2y = 2.
Again, rearrange the equation into slope-intercept form:
4x + 2y = 2
2y = -4x + 2
y = -2x + 1
Plot the y-intercept (0, 1).
Use the slope of -2 to find another point. For example, if we move 1 unit to the right (x = 1), we move 2 units downward (y = -1). Plot this point.
Draw a straight line through these two points.
The graph of the system of equations is the intersection of these two lines.