review the graphs of a system of these two linear equations in two variables: y = 4x - 10 and y = -2x + 8 find the solution of the system
To review the graphs of the system, we need to graph both equations on the same coordinate plane.
The first equation, y = 4x - 10, is in slope-intercept form. This means the graph will be a straight line with a slope of 4, and a y-intercept of -10. To graph it, we can plot the y-intercept, which is the point (0, -10), and then use the slope of 4 to find more points.
By choosing any x-value, we can find the corresponding y-value by substituting it into the equation. For example, if we choose x = 2, the equation becomes y = 4(2) - 10 = 8 - 10 = -2. So, when x = 2, y = -2. Plot this point (2, -2) on the graph.
Next, we can use the slope of 4 to find another point. Since the slope is rise over run, we can move up 4 units and right 1 unit from the point (2, -2) to find a new point. This gives us (3, 2).
Finally, we can connect the points (0, -10), (2, -2), and (3, 2) with a straight line, which represents the graph of the first equation.
Now, let's graph the second equation, y = -2x + 8. Again, this is in slope-intercept form, so the y-intercept is 8. Plot the point (0, 8) on the graph.
To find more points, we can use the slope of -2. From the point (0, 8), we can move down 2 units and right 1 unit to find a new point, giving us (1, 6).
Connect the points (0, 8) and (1, 6) with a straight line, which represents the graph of the second equation.
At this point, we have two lines on the same coordinate plane. The solution of the system is the point where the two lines intersect.
From the graph, it appears that the two lines intersect at the point (2, -2). Therefore, the solution of the system of equations y = 4x - 10 and y = -2x + 8 is x = 2 and y = -2.