To graph the system of linear equations:
1. Graph the equation y = x + 3:
- Plot the y-intercept at (0,3).
- Determine another point by going up 1 unit and right 1 unit from the y-intercept, resulting in (1,4).
- Draw a straight line through these two points to represent the equation.
2. Graph the equation -4x + 4y = 28:
- Rearrange the equation to slope-intercept form: y = x + 7.
- Plot the y-intercept at (0,7).
- Determine another point by going up 1 unit and right 1 unit from the y-intercept, resulting in (1,8).
- Draw a straight line through these two points to represent the equation.
Now, describe what the graph looks like:
- The first line (y = x + 3) intersects the y-axis at (0,3), and it has a positive slope.
- The second line (-4x + 4y = 28 or y = x + 7) intersects the y-axis at (0,7), and it also has a positive slope.
- The two lines are parallel and do not intersect each other at any point.
What the graph tells the solution to the system of linear equations:
- Since the two lines are parallel and do not intersect, there is no solution to the system of linear equations. This means there is no point (x, y) that satisfies both equations simultaneously.
Solve the linear equations by graphing graph on your own in your submitted answer describe what the graph looks like and what tells you the solution to the system of linear equations
Y= x + 3
-4x + 4y = 28
3 answers
Short little answer
The graph shows two parallel lines, indicating that there is no solution to the system of linear equations.