Solve the system by graphing. Then classify the system.?
6x-y=50
6x+7y=-14
What is the solution of the system?
(type an ordered pair. Type N if there is no solution. Type R if the solution is all real numbers)
Subtract the second equation from the first and get
-8y = 64
y = -8
Now use the first equation and the y answer
6x +8 = 50
6x = 42
x = 7
(7, -8)
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To solve the system of equations by graphing, you can create a graph with the x-axis representing the values of x and the y-axis representing the values of y.
For the first equation, 6x - y = 50, we can rearrange it to y = 6x - 50 by adding y to both sides and subtracting 50 from both sides. This equation is in slope-intercept form, y = mx + b, where m is the slope (6 in this case) and b is the y-intercept (-50 in this case).
For the second equation, 6x + 7y = -14, we can rearrange it to y = -(6/7)x - 2 by subtracting 6x from both sides and dividing by 7. Again, this equation is in slope-intercept form.
Now, graph both of these lines on the same coordinate plane. The point where they intersect will represent the solution to the system.
By graphing the two lines, you will find that they intersect at the point (4, 14). So the solution to the system is the ordered pair (4, 14).
To classify the system, you can check the slopes of the lines. In this case, both lines have different slopes, 6 and -(6/7) respectively. Since the slopes are different, the lines intersect and there is a unique solution. The system is classified as consistent and independent.