To graph the system of equations y=3x - 1 and 2x + y = 4, we need to plot the lines represented by each equation on the coordinate plane and find the point of intersection.
For the first equation y=3x - 1, we can assign different values to x and calculate corresponding values for y. Let's choose x = 0, 1, and -1:
When x = 0, y = 3(0) - 1 = -1. So one point on the line is (0, -1).
When x = 1, y = 3(1) - 1 = 2. So another point on the line is (1, 2).
When x = -1, y = 3(-1) - 1 = -4. So another point on the line is (-1, -4).
Plotting these three points and connecting them, we get a line.
For the second equation, 2x + y = 4, we can also choose values for x and calculate corresponding values for y:
When x = 0, 2(0) + y = 4, y = 4. So one point on the line is (0, 4).
When x = 1, 2(1) + y = 4, y = 2. So another point on the line is (1, 2).
When x = -1, 2(-1) + y = 4, y = 6. So another point on the line is (-1, 6).
Plotting these three points and connecting them, we get another line.
Now, we can see where these two lines intersect. The point of intersection is (1, 2).
Therefore, the solution to the system of equations y=3x - 1 and 2x + y = 4 is x = 1 and y = 2.
find the solution to the system of equations by graphing y=3x -1 2x +y=4
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