Question - Graphing Linear Equations to Find Intersection Points
Solution:
To graph each pair of lines from the provided sets A, B, and C, follow these steps for each set:**Set A:**Equations:1. $$y = 2x + 1$$2. $$y = -x + 7$$For each equation, find two points by choosing values for $$x$$ and calculating the corresponding $$y$$ value. Then plot these points on a graph and draw a line through them.Equation 1:Let $$x = 0$$, then $$y = 2(0) + 1 = 1$$. So, one point is (0,1).Let $$x = 1$$, then $$y = 2(1) + 1 = 3$$. Another point is (1,3).These two points will help you graph the first line.Equation 2:Let $$x = 0$$, then $$y = -(0) + 7 = 7$$. One point is (0,7).Let $$x = 1$$, then $$y = -(1) + 7 = 6$$. Another point is (1,6).These two points will help you graph the second line.**Set B:**Equations:1. $$2y + 8 = x$$2. $$4y - 2x = -16$$First, rearrange these equations into slope-intercept form ($$y = mx + b$$).Equation 1:$$x = 2y + 8$$ can be written as $$y = \frac{1}{2}x - 4$$Equation 2:$$4y - 2x = -16$$ can be simplified to $$2y - x = -8$$, which can be written as $$y = \frac{1}{2}x + 4$$Now, find two points for each of these equations using the method shown in set A, and graph them.**Set C:**Equations:1. $$6x - 2y = 20$$2. $$y + 3x - 5 = 0$$First, rearrange these equations into slope-intercept form.Equation 1:$$6x - 2y = 20$$ can be simplified to $$3x - y = 10$$, which can be written as $$y = 3x - 10$$Equation 2:$$y + 3x - 5 = 0$$ can be rearranged to $$y = -3x + 5$$Again, find two points for each equation and graph each line. Please note that I cannot directly graph them here, but this explanation should help you plot them on your own graph paper. Once graphed, you can identify the intersection point of each pair of lines, which is the solution to each set of simultaneous equations.
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