Solve the following system of linear equations by graphing graph on your own piece of paper in your submitted answer describe what the graph looks like and what this tells you about the solution to the system of linear equations y equals x + 3 and -4x + 4y = 28
To solve this system of linear equations by graphing, we first need to rearrange the second equation to solve for y:
-4x + 4y = 28
4y = 4x + 28
y = x + 7
Now we can graph both equations on the same set of axes.
The first equation y = x + 3 is a line with a y-intercept of 3 and a slope of 1. This means that it will pass through the point (0,3) and will increase by 1 unit on the y-axis for every 1 unit it increases on the x-axis.
The second equation y = x + 7 is a line with a y-intercept of 7 and a slope of 1. This means that it will pass through the point (0,7) and will increase by 1 unit on the y-axis for every 1 unit it increases on the x-axis.
When we plot both equations on the same set of axes, we see that the two lines intersect at the point (2,5). This point represents the solution to the system of linear equations.
In conclusion, the graph of the system of equations shows that there is one unique solution, where the two lines intersect at the point (2,5). This means that the system of linear equations has a single solution, and that solution is x = 2 and y = 5.