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 equations. y=x+3 −4x+4y=28
To solve the system of linear equations, we can first rewrite the equations in slope-intercept form:
1) y = x + 3
2) 4y = 4x + 28
y = x + 7
Now, we can graph these two equations on the same coordinate plane.
The first equation, y = x + 3, has a y-intercept of 3 and a slope of 1. This means the line will pass through the point (0, 3) and have a slope of 1, sloping upwards.
The second equation, y = x + 7, has a y-intercept of 7 and a slope of 1. This line will pass through the point (0, 7) and also slope upwards.
When we graph these two lines, we see that they are parallel lines that do not intersect. This means the system of linear equations has no solution, as there is no point that satisfies both equations.
Therefore, the graph tells us that the system of equations is inconsistent and has no solution.