Using a graph, solve for x and y below.
If 6x - 3y = 24
&
18x + 3y = 12
I know to use the forumla y = m*x + b. I also know to assume x=0 so that your starting point is (0,b) with b representing the y axis. M represents slope, which is rise over run. What I am having trouble with is working one of the equations so it fits the formula in. Any help or insight would be greatly appreciated. Thanks!
You don't have to use any particular form of the equation.
In fact, this problem asks you to graph the lines, and solve the system of equations using the graphs.
For example,
http://www.wolframalpha.com/input/?i=plot+6x+-+3y+%3D+24+%2C+18x+%2B+3y+%3D+12+
My apologies. I guess I didn't word my question properly. The instructor needs us to show our work, so I have to show how I get the starting points on the graph.
Here is what I have so far. Maybe you can see where I am going wrong.
18x+3y=12
3y=18x+12
y=-18x+4
This gives me starting points of (0,4)
6x-3y=24
-3y=-6x+24
-y=2x-8
y=-2x+8
This gives me starting points of (0,8)
For the first equation, I would use the starting point, then go down 18 and to the right 1. Same for the second: down 2, 1 to the right.
That doesn't match the graph you linked to, and I can't seem to figure out where the mistake is being made.
each graph is a line. You don't need to use y=mx+b to "start."
18x+3y=12
or,
6x+y=12
If x=0, y=12
if y=0, x=2
So, plot the points (0,12) and (2,0) and join them in a line.
Using the Ax+By=C (standard) form is very convenient, since you can easily get both intercepts just by making one of the variables zero.
For the first one, if you go down 18 and to the right 1, you are plotting a line with slope -18. But the slope is really -6. You did not divide the 18 by 3, as you did the other terms.
To solve the given system of equations using a graph, we can start by rearranging each equation in the form y = mx + b, where m represents the slope and b represents the y-intercept.
Let's begin with the first equation:
6x - 3y = 24
To isolate y, we can subtract 6x from both sides of the equation:
-3y = -6x + 24
Now, divide both sides of the equation by -3 to solve for y:
y = (-6x + 24) / -3
y = 2x - 8
Now, let's move on to the second equation:
18x + 3y = 12
Again, let's isolate y by subtracting 18x from both sides:
3y = -18x + 12
Divide both sides of the equation by 3 to solve for y:
y = (-18x + 12) / 3
y = -6x + 4
Now we have both equations in the form y = mx + b. The first equation, y = 2x - 8, has a slope of 2 and a y-intercept of -8. The second equation, y = -6x + 4, has a slope of -6 and a y-intercept of 4.
To graph these equations, choose values for x and calculate the corresponding values for y.
For the first equation, let's assume x = 0:
y = 2(0) - 8
y = -8
So the first point on the graph is (0, -8).
Now, assume x = 3:
y = 2(3) - 8
y = -2
The second point is (3, -2).
For the second equation, let's assume x = 0:
y = -6(0) + 4
y = 4
So the third point is (0, 4).
Assume x = 3:
y = -6(3) + 4
y = -14
The fourth point is (3, -14).
Plot these points on a graph and draw a straight line through them. The point where the two lines intersect is the solution to the system of equations.