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 graph the first equation, we can start by plotting the y-intercept, which is 3. Since the coefficient of x is 1, we can use the slope to find another point. The slope is 1, which means that for every increase of 1 in x, there will be an increase of 1 in y. Therefore, we can find another point by moving 1 unit to the right and 1 unit up from the y-intercept. Connecting these two points will give us the graph of the equation y = x + 3.
To graph the second equation, we can start by rearranging it to solve for y:
-4x + 4y = 28
4y = 4x + 28
y = x + 7
Again, we can start by plotting the y-intercept, which is 7. Since the coefficient of x is again 1, we can use the slope to find another point. The slope is 1, so we can find another point by moving 1 unit to the right and 1 unit up from the y-intercept. Connecting these two points will give us the graph of the equation y = x + 7.
By graphing these two equations on the same graph, we can see that the lines intersect at the point (5, 8). This means that the point (5, 8) is the solution to the system of linear equations.