Question
Review the graphs of a system of two linear equations and two variables 4x + 3y = 15 and y = x + 5
Answers
Answered by
GPT 3.5
To analyze the system of linear equations 4x + 3y = 15 and y = x + 5, we can start by graphing each equation individually.
First, for the equation 4x + 3y = 15, we need to find two points that satisfy the equation. We can choose to set x = 0 and solve for y, and then set y = 0 and solve for x.
When x = 0:
4(0) + 3y = 15
3y = 15
y = 5
So, one point on the graph is (0,5).
When y = 0:
4x + 3(0) = 15
4x = 15
x = 15/4 = 3.75
Another point on the graph is (3.75, 0).
Now, let's graph the line 4x + 3y = 15:
Plot the points (0,5) and (3.75,0) and draw a line passing through those points.
Next, for the equation y = x + 5, we can easily graph this line by identifying its y-intercept, which is 5.
Therefore, plot the point (0,5) for the equation y = x + 5.
Now we can see the graphs of the two equations intersect at the point (2,7). This point represents the solution to the system of equations 4x + 3y = 15 and y = x + 5.
First, for the equation 4x + 3y = 15, we need to find two points that satisfy the equation. We can choose to set x = 0 and solve for y, and then set y = 0 and solve for x.
When x = 0:
4(0) + 3y = 15
3y = 15
y = 5
So, one point on the graph is (0,5).
When y = 0:
4x + 3(0) = 15
4x = 15
x = 15/4 = 3.75
Another point on the graph is (3.75, 0).
Now, let's graph the line 4x + 3y = 15:
Plot the points (0,5) and (3.75,0) and draw a line passing through those points.
Next, for the equation y = x + 5, we can easily graph this line by identifying its y-intercept, which is 5.
Therefore, plot the point (0,5) for the equation y = x + 5.
Now we can see the graphs of the two equations intersect at the point (2,7). This point represents the solution to the system of equations 4x + 3y = 15 and y = x + 5.