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
To solve this system of linear equations by graphing, we first need to rearrange both equations in slope-intercept form (y = mx + b).
1) y = x + 3
2) −4x + 4y = 28
For equation 2, we can divide through by 4 to simplify it:
-1x + y = 7
y = x + 7
Now we can graph these two equations on a coordinate plane.
The graph of equation 1 (y = x + 3) is a straight line with a slope (m) of 1 and a y-intercept (b) of 3. This means that for every increase of 1 in the x-coordinate, the y-coordinate increases by 1. The line passes through the point (0,3).
The graph of equation 2 (y = x + 7) is another straight line with a slope of 1 and a y-intercept of 7. This line also increases by 1 in the y-coordinate for every increase of 1 in the x-coordinate. It passes through the point (0,7).
When we graph these two lines, they intersect at the point (4, 7). This is the solution to the system of linear equations.
The graph shows that there is a unique solution to the system, as the two lines intersect at a single point.