Here is what I have done so far with thes two equation that I need to slove by graphing
2x+y=5 y=5-2x
3x-y=10 -y= 10- 3x
I have substituted y= 5-2x into the second equation
3x- (5-2x)=10
5x+5=10
x=1
Here I got lost and don't know what to do next in plotting the graph. Thanks for you help
To graph these equations, you need to plot the points that satisfy each equation and then connect them to form the line.
Let's start by solving the first equation: 2x + y = 5.
To plot this equation, you can choose a few different values for x and then calculate the corresponding values for y. For example, you can let x = 0, which gives you y = 5. This means that one point on the line is (0, 5).
Then, let's choose another value for x, such as x = 2. Plugging this value into the equation, we get 2(2) + y = 5, which simplifies to 4 + y = 5. Solving for y, we find that y = 1. Therefore, another point on the line is (2, 1).
Plot these two points on your graphing paper and connect them with a straight line. This line is the graphical representation of the equation 2x + y = 5.
Now, let's solve the second equation: y = 5 - 2x.
Similarly, choose a few values for x and calculate the corresponding values for y. Using the same values of x as before, we can fill out the table:
x | y
0 | 5
2 | 1
Plot these points on the same graphing paper and connect them with a different line. This line represents the equation y = 5 - 2x.
Now, we need to find their point of intersection, which tells us the solution to the system of equations. In this case, the point of intersection is (1, 3), which means that x = 1 and y = 3 simultaneously satisfy both equations.
Plot this point on the graph as well. The point (1, 3) is the solution to the system of equations.
To summarize, you graphed the equations 2x + y = 5 and y = 5 - 2x by choosing values for x, calculating corresponding values for y, and plotting the points. The lines that pass through these points represent the equations. The point where these lines intersect is the solution to the system.