To begin, let's rearrange the second equation to solve for y:
-4x + 4y = 38
4y = 4x + 38
y = x + 9.5
Now, we have the two equations as:
y = x + 3
y = x + 9.5
When graphing these two linear equations, we see that they have different slopes (1 for y=x+3 and 1 for y=x+9.5), which tells us that the lines are not parallel and will intersect at some point.
Graphically, the line for y=x+3 has a y-intercept of (0,3) and a slope of 1, meaning every time x increases by 1, y increases by 1. The line for y=x+9.5 has a y-intercept of (0,9.5) and a slope of 1, meaning it also increases by 1 each time x increases by 1.
When we graph these lines on a graph, we will see that they intersect at a point where x and y have the same values for both equations. This point is the solution to the system of equations.
After graphing them, we find that the two lines intersect at the point (6,9), indicating that x=6 and y=9 satisfies both equations. Therefore, the solution to the system of linear equations is x=6 and y=9.
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=38
1 answer
1 answer