how and where do I start to solve x-3y=5

Question

I need help with algebra equations, for some reason I am having a problem retaining the solutions.

 

One of the equations is x-3y=5  and I am problems with roots the main equation is the root of 112.

 

on x-3y=5 I gave x the value of 0 so I have 3*0= 0 so now I have to change over and give -3 or take -3 and 0 and divide each side by -3, but I am not sure what to do from there.

 

Can someone help me?

Answer 1

Hello Vicky,

The equation you have is a Linear Equation, meaning that it will produce a line on a coordinate graph.  So in order to solve it you need to either create a table of values that make it true like you have tried or find the slope and the y-intercept and then graph it to find solutions.  I would do the second option but it depends on your instructions and what you have learned so far.

 

To find the slope I would manipulate the equation until it is in the Slope-Intercept form y = mx + b, where "m" is the slope and the "b" is the y-intercept, (0,b).

1. Subtract "x" from both sides of the equation yielding -3y = 5 - x

2. Now just so that it matched the form we want, turn around the left side to yield -3y = -x + 5

3. Now divide by -3 on both sides or if you prefer you can multiply by -1/3 yielding -3/-3 y = -1/-3 x + 5/-3

4. Now simplify to yield y = 1/3 x - 5/3

So the m or slope is 1/3 and the y-intercept is at (0,-5/3 or -1 2/3)

Do you know how to graph that?  If not then plot the y-intercept on the y-axis at - 1 2/3 and then move down 1 unit (because it is negative) and 3 units to the right (from the slope - do you need slope explained?).  Plot a point there and draw the line.  The line is the solution to this equation but if you need actual points - (x,y) then find points on the graph where it is easy to determine the coordinates of the point and list them in a table of values.  Do you know how to do that?

 

Vicky, are you supposed to find the x- and y- intercepts?  If so, you set y = to zero for the x-intercept which looks like this:

 

x -3(0) = 5

x-0 = 5

x=5

So the x-intercept is at (5,0)

 

To find the y-intercept, set x = to zero:

 

0 - 3y = 5

-3y = 5

then divide both sides by -3

(-3)/(-3) y = 5/(-3)

 

y = 5/(-3)

y = -5/3 or - 1 2/3

So the y-intercept is (0, -1 2/3)

 

Is this what you need?

 

Pam W.