Find the point of intersection by graphing both lines and observing where they intersect.
Y = -4x + 2
Y = x - 3
To find the point of intersection, we can set the two equations equal to each other and solve for x.
-4x + 2 = x - 3
Adding 4x to both sides, we get:
2 = 5x - 3
Adding 3 to both sides, we get:
5 = 5x
Dividing both sides by 5, we get:
x = 1
Now, substitute this value of x back into either equation to find the corresponding y-value:
Y = x - 3
Y = 1 - 3
Y = -2
Therefore, the point of intersection is (1, -2).
Now, let's graph the two equations to visually verify the point of intersection.
Plotting the points (0, 2) and (1, -2) on a coordinate plane and drawing a straight line through them, we get the graph of the equation Y = -4x + 2.
Similarly, plotting the points (0, -3) and (1, -2) on the coordinate plane and drawing a straight line through them, we get the graph of the equation Y = x - 3.
By observing the intersection of the two lines, we can conclude that the point of intersection is indeed (1, -2).