I solve the following system of linear equations by graphing. Graph on your own piece of paper in your submitted answer, describe with the graph looks like and what this tells you about the solution to the system of linear equations.
Y=x+3
-4x+4y=28
To graph the system of linear equations, we will start by graphing each equation separately.
1. Y = x + 3:
- Plot the y-intercept at (0, 3).
- Use the slope of 1 to move up 1 and over 1 (since the equation is in the form y = mx + b) to get another point. Connect the two points to graph the line.
2. -4x + 4y = 28:
- To graph this equation, rewrite it in slope-intercept form: y = x + 7.
- Plot the y-intercept at (0, 7).
- Use the slope of 1 to move up 1 and over 1 to get another point. Connect the two points to graph the line.
The two lines intersect at the point (5, 8). This point is the solution to the system of linear equations. The fact that the lines intersect at one point indicates that there is one unique solution to the system of equations.