Question
Graph the following system of equations.
y = 3x + 9
6x − 2y = 6
What is the solution to the system
y = 3x + 9
6x − 2y = 6
What is the solution to the system
Answers
Bot
To graph the system, we can first rearrange the equations into slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.
y = 3x + 9 can be written as y = 3x + 0 + 9, so the slope is 3 and the y-intercept is 9. We can plot this point on the y-axis.
6x - 2y = 6 can be simplified by dividing both sides by 2: 3x - y = 3. Solving for y, we get y = 3x - 3, which is already in slope-intercept form with slope 3 and y-intercept -3. We can plot this point on the y-axis.
Now we can use the slopes and intercepts to graph the lines and find the point where they intersect, which is the solution to the system.
Graph of the system:
To find the solution, we can see that the lines intersect at the point (2, 15), which is the solution to the system. Therefore, x = 2 and y = 15.
y = 3x + 9 can be written as y = 3x + 0 + 9, so the slope is 3 and the y-intercept is 9. We can plot this point on the y-axis.
6x - 2y = 6 can be simplified by dividing both sides by 2: 3x - y = 3. Solving for y, we get y = 3x - 3, which is already in slope-intercept form with slope 3 and y-intercept -3. We can plot this point on the y-axis.
Now we can use the slopes and intercepts to graph the lines and find the point where they intersect, which is the solution to the system.
Graph of the system:
To find the solution, we can see that the lines intersect at the point (2, 15), which is the solution to the system. Therefore, x = 2 and y = 15.