How do you find the solution to a system of equations graphically?
A Find the slope of the two lines.
B Find the y-intercept of the two lines.
C Find the slope and y-intercept of the two lines.
D Find the point where the two lines intersect.
D Find the point where the two lines intersect.
D Find the point where the two lines intersect.
The correct answer is D - Find the point where the two lines intersect.
To find the solution to a system of equations graphically, you need to plot the equations as lines on a coordinate plane. Then, you can determine the point of intersection, which represents the solution.
Here is a step-by-step explanation of how to find the solution to a system of equations graphically:
1. Write down the given system of equations in the form y = mx + b, where m is the slope of the line and b is the y-intercept.
2. Plot the two lines on a coordinate plane using the slope-intercept form. To do this, start by plotting the y-intercept for each equation as a point on the y-axis.
3. Determine the slope for each line. The slope represents the change in y divided by the change in x. For example, if the slope is 2/3, it means that for every 3 units moved horizontally (x-axis), the line rises 2 units vertically (y-axis).
4. Use the slope to plot additional points on each line. Start from the y-intercept, and using the slope, move horizontally and vertically to locate more points. Connect these points to form the lines.
5. Locate the point(s) where the two lines intersect. This is the solution to the system of equations. If the lines do not intersect, it means there is no solution.
By following these steps, you can determine the solution to a system of equations graphically by identifying the point of intersection of the lines.