substitution and elimination

Question

solve using substitution or elimination

3x+5y=2

2x-y=-3

Answer 1

Solving the second equation for Y:

 

   2x + 3 = Y

 

substituting this into the first equation:

 

 3x + 5 ( 2x +3) = 2

3x + 10x + 15 = 2

13x + 15 = 2

13x = -13

x = -1

Y = 2x + 3 = 2(-1) +3 = -2 + 3 = 1

 

Check:   1st equation:   3(-1) + 5(1) = -3 + 5 = 2

              2nd equation: 2(-1) - 1 = -2 - 1 = -3

 

If you want to do it using elimination, multiply the first equation by -2

and the second equation by 3. Then add

 

-6x + -10y = -4

 6x      - 3y =  -9

---------------------------

 

           -13y  = -13

              y =1

 

Substituting this into the second equation:

  2x - 1 = -3

  2x   = -2

    x = -1