Solve each system of equation by multiplying first.

1.) 2x+y=3
-x+3y=-12

2.) 6x+5y=19
2x+3y=5

3)2x+5y=16
-4x+3y=20

1.  2x + y = 3
     -x + 3y = -12  => multiply by 2

     2x + y = 3
    2(-x) + 2(3y) = 2(-12)

     2x + y = 3
    -2x + 6y = -24    Now add the equations

           7y = -21
             y = -3    Substitute back into equation

2x + y = 3
2x + (-3) = 3
2x = 6
x = 6/2 = 3

(3, -3)

2.  6x + 5y = 19
     2x + 3y = 5    => multiply by -3 so the x's will cancel

     6x + 5y = 19
(-3)2x + (-3)3y = -3(5)

     6x + 5y = 19
    -6x - 9y = -15      now add the 2 equations

          -4y = 4
             y = -1         now substitute back into the equation

2x + 3y = 5
2x + 3*-1 = 5
2x - 3 = 5
2x = 8
x = 8/2 = 4

(4,-1)

3.  2x + 5y = 16  => multiply by 2 so x's cancel
    -4x + 3y = 20

(2)2x + (2)5y = (2)16

 4x + 10y = 32
-4x + 3y  = 20      add the equations

         13y = 52
           y = 52/13 = 4  substitute into unchanged equation

-4x + 3(4) = 20
-4x + 12 = 20
-4x = 8
x = 8/-4 = -2

(-2, 4)

J= r + 9 because since jessica rode 9 more miles than roger, you add 9 miles to rogers mileage.