Final answer:
To solve the system by graphing, plot both equations on the same graph to find the intersection point. Construct a table for each equation to find the points to plot. Then check each option by plugging x and y values into both equations to find the pair that satisfies both.
Step-by-step explanation:
To solve the system by graphing, you would graph each equation on the same set of axes and look for the point where the two lines intersect. The given system of equations is:
To graph the first equation, you would first solve for y.
y = -2x + 3
This line has a slope (m) of -2 and a y-intercept (b) of 3. For the second equation, y = x - 3, the slope is 1 and the y-intercept is -3. You can construct a table for each equation and plot the points. After graphing both lines, the solution to the system is the point where both lines intersect.
The correct point of intersection, from the given options, can be determined by substituting x and y values into the equations to see which pair satisfies both equations. For example, if you choose point (-2, -1), by plugging it into both equations:
2(-2) + (-1) = -4 - 1 = -5 ≠ 3 (does not satisfy the first equation)
-1 = -2 - 3 = -5 (does not satisfy the second equation)
This process is repeated for all options to find the correct solution.