<PRE><B>Question 74261</B>
&lt;pre&gt;
1. Solve by elimination method 
4x - y = -3 
y - 3 = 4x 

Rewrite the equation in standard form:
         4x - y = -3
         4x - y = -3
        _____________

         4x - y = -3
        -4x + y = +3
        _____________
          0 + 0 = 0

The equations are the same so there are many solution. 
The graph are same line
Let us look at the graph to check if there is a solution


{{{graph (200, 200, -4, 6, -5, 5, 4x+3, 4x+3)}}}



2. Solve by graphing method
x - y = 3
x + y = 1 

To graph it easily, we will rewrite the equation in slope - intercept form
y = mx + b, where m = slope and b = y -intercept

x - y = 3 -------&gt;        y =  x - 3  eq1, where m = 1 and b = -3
x + y = 1 -------&gt;        y = -x + 1  eq2, where m = -1 and b = 1

To graph eq1 the first point is (0,-3). use the slope the locate second point
m=1 means move 1 unit up and 1 unit right. then draw a line

To graph eq2 the first point is (0,1). use the slope to locate the 2nd point
m=-1 means move 1 unit down and 1 unit right or 1 unit up and 1 unit left
then draw a line.
the graph looks like this:

{{{graph (200, 200, -3, 4, -4, 5, x-3, -x+1)}}}

Solution is (2, -1). the graph intersect when x = 2 and y = -1.



3. Solve by addition method
We use this method so that one variable will be eliminated.
           1/5x + 2/3y = -8/5      eq1
                3x - y = 9         eq2
            
Simplify eq1. Mutiply LCD -15 each term (eq1 only)
              3x + 10y = -24   eq1
              3x -   y =  9    eq2
             _______________

Notice, if we add the two equations, no variable will be eliminated

So we must multiply a certain number to do that
say we eliminate x,Multiply -1 eq2 
             
               3x + 10y = -24
            -1(3x -   y =  9)
             _______________


              3x + 10y = -24
             -3x +   y = -9
             _______________
               0 + 11y = -33  divide both sides by 11

                     y = -3

Substitute y = -3 to any of the equations
                 3x -   y =  9
                 3x -(-3) =  9
                   3x + 3 = 9    subtract 3 both sides
                       3x = 6    Divide 3 both sides
                        x = 2

Solution is (2,-3). The graph intersect when x = 2 and y = -3

Checking:

{{{graph (200, 200, -3, 5, -6, 5, 3x-9, -(3/10)x-(12/5))}}}
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