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













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 ------->        y =  x - 3  eq1, where m = 1 and b = -3

x + y = 1 ------->        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:







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:





 

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