Solve the following systems of equations graphically. Please state your answer as an ordered pair (x,y).
(Do not put spaces between any part of your answer, or it will not be graded as correct.)
To solve a system of equations graphically, you need to plot the equations on a coordinate plane and find the point where they intersect. This point represents the solution to the system of equations.
Let's say we have a system of equations with two equations:
Equation 1: y = 2x + 1
Equation 2: y = -x + 3
To solve this system graphically, we will plot the two equations on a coordinate plane.
1. Plot the first equation, y = 2x + 1:
- Choose some x-values and substitute them into the equation to find their corresponding y-values.
- For example, when x = 0, y = 2(0) + 1 = 1. So plot the point (0, 1).
- Repeat this process for a few more x-values to get multiple points on the line.
2. Plot the second equation, y = -x + 3:
- Again, choose some x-values and substitute them into the equation to find their corresponding y-values.
- For example, when x = 0, y = -(0) + 3 = 3. So plot the point (0, 3).
- Repeat this process for a few more x-values to get multiple points on the line.
Now that you have plotted both equations, observe the point of intersection between the two lines. This point represents the solution to the system of equations.
In this case, the lines intersect at the point (1, 3). Hence, the solution to the system of equations is x = 1 and y = 3.
So the answer, in the form of an ordered pair, is (1, 3).