"Determine the point of intersection of each pair of equations by plotting accurate graphs."
This question asks to 'determine' the point of intersection by plotting accurate graphs. I'm not sure how one is supposed to be able to 'determine' the point of intersections just by plotting the equations on graphs without simultaneously solving them for x and y... Quite confused...
If you've been asked to determine the intersection by 'plotting accurate graphs', then it seems like you're expected to plot the given equations on graph paper, and then check the x and y co-ordinates of the point of intersection on your graph, rather than solving the equations directly.
I understand your confusion. When solving a system of equations by plotting accurate graphs, we can visually determine the point of intersection, which represents the solution to the system. Here's how you can approach this problem:
1. Start by selecting two equations, for example:
Equation 1: y = 2x + 3
Equation 2: y = -x + 5
2. Plot the graphs of both equations on the same coordinate plane. To do this, create a table of values for each equation and plot the corresponding points.
For Equation 1 (y = 2x + 3):
- Choose a few x-values and calculate the corresponding y-values. For example:
- If x = 0, then y = 2(0) + 3 = 3.
- If x = 1, then y = 2(1) + 3 = 5.
For Equation 2 (y = -x + 5):
- Choose a few x-values and calculate the corresponding y-values. For example:
- If x = 0, then y = -(0) + 5 = 5.
- If x = 1, then y = -(1) + 5 = 4.
3. Plot the calculated points on the graph for each equation. Connect the points to form a straight line for each equation.
4. The point where the two lines intersect represents the solution to the system of equations. To determine the coordinates of this point, visually inspect the graph and note the coordinates of the intersection point.
By following this method, you can determine the point of intersection of the two equations. Keep in mind that this approach may not give you exact coordinates, but it will provide a good estimate based on the accuracy of your graph. If you need more precise solutions, you can use algebraic methods such as substitution or elimination to solve the system of equations analytically.