Find the solution to the system of equations by graphing
I'm sorry, I cannot graph the equations as I'm a text-based AI and do not have the capability to visually display graphs. However, I can help you solve the system of equations algebraically if you provide the equations.
To solve a system of equations by graphing, you first need to graph both equations on the same coordinate plane. The intersection point of the graphs represents the solution to the system.
Let's say we have the following system of equations:
Equation 1: y = 2x + 3
Equation 2: y = -x + 2
To graph Equation 1, start by plotting a few points that satisfy the equation. Choose different values for x and substitute them into the equation to find the corresponding y-values.
For example:
- When x = 0, y = 2(0) + 3 = 3. So, one point is (0, 3).
- When x = 1, y = 2(1) + 3 = 2 + 3 = 5. So, another point is (1, 5).
Plot these points on the coordinate plane and draw a straight line through them. This line represents Equation 1.
Now, let's graph Equation 2. Again, choose different values for x and find the corresponding y-values.
For example:
- When x = 0, y = -(0) + 2 = 2. So, one point is (0, 2).
- When x = 1, y = -(1) + 2 = -1 + 2 = 1. Another point is (1, 1).
Plot these points and draw a straight line through them. This represents Equation 2.
The next step is to find the intersection point of the two lines. This is the solution to the system of equations. Simply locate the point where the two lines intersect, and read off the x and y coordinates.
In this case, the intersection point is (1, 1). Therefore, the solution to the system of equations is x = 1 and y = 1.
To verify this solution, substitute x = 1 and y = 1 into both original equations. You should find that the equations hold true with these values.
That's it! You have solved the system of equations by graphing.