okay
i am getting confuse with the decimals and fractions in order to make a table for the following problem.can someone help me make the tables
the problem reads as follows.
solve the system.
5x-3y=13
4x-3y=11
Now, i know i have to break them to the form of y=mx+b
inorder to graph and see the intersection to be my solution but i am trying to do the table and i get continues decimals.
If you are plotting them, what problem is the decimals? Graphing solutions are never exact, at least here in Texas.
IF I DON'T PLOT THEM BECAUSE ITS NOT ASKING FOR A GRAPH BUT JUST TO STATE THE SOLUTION IS THERE ANOTHER WAY OF FINDING THAT OUT.
Don't get caught up in the same rigorous way of doing things, intuition is an important part of doing math
Perhaps leaving your first equation in the form y =(5x-13)/3 might help
you know that for y to be an integer value, the numerator of the right side has to be divisible by 3 (a multiple of 3 such as 6,9,12,...)
if x=-1 then the top is -18 which divides evenly by 3 to give a y value of
-6. Now you have an ordered pair to plot, here comes the easy part....
you know the slope is 5/3 which is rise/run (rise is y, run is x)
so if you increase the x by 3 to get 2
and increase the y by 5 to get -1 you have a new integer point (2,-1)
The key thing is:
If you find a starting point with integer values, and you know the slope, you can then find other integer valued points by simply adding the rise and run values.
(if the slope is negative, make either the x or the y negative, not both, and add that way)
To solve the system of equations 5x - 3y = 13 and 4x - 3y = 11 without graphing, you can use the method of substitution. Here's how:
1. Start with one of the equations and solve it for one variable in terms of the other. Let's use the first equation: 5x - 3y = 13.
Solving for x, we have x = (13 + 3y) / 5.
2. Substitute this expression for x into the second equation: 4x - 3y = 11.
Replace x with (13 + 3y) / 5, we get:
4((13 + 3y) / 5) - 3y = 11.
3. Simplify this equation. Multiply 4 to both terms inside the parentheses, we have:
(52 + 12y) / 5 - 3y = 11.
4. Multiply through by 5 to eliminate the fraction:
52 + 12y - 15y = 55.
Simplifying, we have:
-3y = 3.
5. Divide both sides by -3 to solve for y:
y = -1.
6. Substitute this value of y back into either of the original equations to find x. Let's use the first equation:
5x - 3(-1) = 13.
Simplifying, we have:
5x + 3 = 13.
Subtracting 3 from both sides, we get:
5x = 10.
Dividing both sides by 5, we have:
x = 2.
So the solution to the system of equations is x = 2 and y = -1.