Could someone please help me with this. I am confused. Math is a weak point for me.
Solve the system of equations by graphing. Then classify the system. 9x-6y=30, 6x-9y= -30. The solution is? Consistent or inconsistent, dependent or independent?
How would I graph this?
Thanks.
9x-6y=30, 6x-9y= -30
divide everything by 3
3x - 2y = +10 multiply by 3
2x - 3y = -10 multiply by 2
9x - 6y = +30
4x - 6y = -20 now subtract
-----------------
5 x = 50
x = 10
20 - 3y = -10
3 y = 30
y = 10
straight lines
intersection at (10,10)
slope of first = 9/6 = 1.5
slope of second = 2/3 = .6667
first hits y axis at -5 and x axis at 10/3
second hits y axis at 10/3 and x axis at -5
To solve the system of equations by graphing, you would need to plot the graph of each equation on the same coordinate plane.
Let's start with the first equation, 9x - 6y = 30. To plot this equation, you can rewrite it in the slope-intercept form (y = mx + b) by isolating y:
9x - 6y = 30
-6y = -9x + 30
y = (9/6)x - 5
y = (3/2)x - 5
Now, pick two values for x (e.g., x = 0 and x = 4) and substitute them into the equation to find the corresponding y-values. Plot these points on the graph and draw a straight line passing through them. Repeat the same process for the second equation, 6x - 9y = -30.
Once you have both lines on the same graph, analyze their intersection point(s). If the lines intersect at a single point, that is the solution to the system of equations. If the lines are parallel and do not intersect, the system is inconsistent and has no solution. If the lines coincide or overlap, the system is dependent, and there are infinitely many solutions.
Now, let's analyze the intersection of the two equations:
The first equation, y = (3/2)x - 5, has a slope of 3/2, meaning as x increases by 2, y increases by 3.
The second equation, 6x - 9y = -30, can be rewritten as y = (2/3)x + 10/3. It also has a slope of 2/3.
By comparing the slopes, we can see that the lines are parallel, and therefore, they do not intersect. This means that the system of equations is inconsistent and has no solution.
In conclusion, the system of equations 9x - 6y = 30 and 6x - 9y = -30 is inconsistent and has no solution.