To graph the system of linear equations, we need to plot the points that satisfy the equations and then connect them to form the lines.
For the equation y=x+3, we can find several points that satisfy the equation. When x=0, y=3. When x=1, y=4, and so on. Plotting these points and connecting them will give us a line that starts at (0,3) and has a slope of 1 (rise of 1 and run of 1).
For the equation -4x+4y=28, we can rearrange it to y=x+7. Similarly, we can find points that satisfy this equation. When x=0, y=7. When x=1, y=8, and so on. Plotting these points and connecting them will give us a line that starts at (0,7) and has a slope of 1.
On the graph paper, we can plot these lines and see where they intersect. The point of intersection represents a solution to the system of linear equations.
The graph of the two lines will look like two straight lines intersecting at one point. This tells us that there is one unique solution to the system of linear equations. The point of intersection is the coordinates of this solution.
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=x+3
−4x+4y=28
1 answer