Solve graphically y = 2x - 6 and y = -2x + 10
can't do graph work here
To solve the system of equations graphically, we will plot the graphs of the two equations on the same coordinate axis and find the point where they intersect. The coordinates of the intersection point will be the solution to the system.
The first equation is y = 2x - 6. To graph this equation, we can use the slope-intercept form y = mx + b, where m is the slope and b is the y-intercept.
The slope of the line is 2, which means that for every 1 unit increase in x, y increases by 2. The y-intercept is -6, which is the point where the line crosses the y-axis.
Plot the y-intercept point (0, -6) on the graph. Then, using the slope of 2, we can find more points on the line. For example, if we move 1 unit to the right (increase x by 1), we move 2 units up (increase y by 2). Thus, we can plot the point (1, -4). Similarly, we can find the point (2, -2) and so on.
Now, let's graph the second equation, y = -2x + 10. Again, we use the slope-intercept form where the slope is -2 and the y-intercept is 10.
Plot the y-intercept point (0, 10) on the graph. Then, using the slope of -2, we can find more points on the line. As we move 1 unit to the right (increase x by 1), we move 2 units down (decrease y by 2). Plot the point (1, 8), (2, 6), and so on.
After plotting both equations on the same graph, you will notice that the lines intersect at a point (x, y). These coordinates represent the solution to the system of equations.
In this case, the intersection point is (2, -2). Therefore, the solution to the system of equations is x = 2 and y = -2.