Solve the following system of linear equations by graphing graph on your own piece of paper and your submitted answer. Describe what the graph looks like and what this tells you about the solution of the system to linear questions. Why equals x + 3 and -4x + 4y = 28?
To solve the system of linear equations by graphing, let's start by rewriting the equations in slope-intercept form:
Equation 1: y = x + 3
Equation 2: -4x + 4y = 28
For Equation 2, rearranging it into slope-intercept form, we have:
4y = 4x + 28
y = x + 7
Now we have both equations in the form y = mx + b, where m represents the slope and b represents the y-intercept.
The graph of Equation 1, y = x + 3, has a slope of 1 and a y-intercept of 3. This means that the line will pass through the point (0,3) and has a slope of 1 (meaning that for every increase of 1 in x, there is a corresponding increase of 1 in y).
The graph of Equation 2, y = x + 7, also has a slope of 1 but a y-intercept of 7. This means that the line will pass through the point (0,7) and has a slope of 1 (similar to Equation 1).
Since both equations have the same slope, the lines will be parallel in the graph. This indicates that the system of equations has no solution. In other words, there is no point where the two lines intersect.
Therefore, the solution to the system of linear equations is empty or null.