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
Negative 4X plus 4Y equals 28
To graph the first equation, y = x + 3, we can start by plotting the y-intercept at (0,3) and then using the slope of 1 to find another point. So, we go up 1 unit and to the right 1 unit to find another point. This gives us a line that increases diagonally upwards from left to right.
For the second equation, -4x + 4y = 28, we want to rewrite it in slope-intercept form y = mx + b. Dividing by 4 on both sides, we get y = x + 7. This line has a y-intercept at (0,7) and a slope of 1, which means it is parallel to the first line but is 4 units above it.
When we graph both lines on the same set of axes, we will see that they are parallel and do not intersect. This means there is no solution to the system of linear equations since the lines are parallel and will never cross each other.
In conclusion, the graph of the system of linear equations of y = x + 3 and -4x + 4y = 28 shows two parallel lines that do not intersect, indicating that there is no solution to the system.