addition method 5x-5y=20, -3x-2y=-12

Question

 can you solve this one with steps because I still don't understand it?

Answer 1

Asterly,

 

It sounds like you want to solve this by elimination.

 

first you manipulate one of both of these formulas so that they end up with terms that can be eliminated by addition.

 

3 times 5x-5y=20 is                  15x-15y=60

5 times -3x-2y=-12 is              -15x-10y=-60

Add the corresponding terms:        -25y=0 or y=0

Substitute 0 for y in either equation to solve for x. 5x=20 or x=4

Try the solution values in the other equation to make sure it makes sense. -3(4)-2(0)=-12 or -3(4)=-12. Looks like the solution makes sense.

                                        

Answer 2

These two equations are the equations of two lines.  To 'solve' them means to find the point that is on both lines (the point where they intersect).  Be careful, because some lines are parallel and never intersect.

 

The problem gives the two equations in "Standard Form"   Ax + By = C

       5x - 5y = 20     eq1

      -3x - 2y = -12    eq2

 

"addition method" means to add the two equations (because adding the same amount to both sides leaves the equation still equal).

 

Often, the problem has coefficients of either x or y that quickly may be made opposite so that they will add to 0.  This problem is a little harder, so multiply each equation by the x coefficient (or -x) in the other equation.

 

       (3)5x - (3)5y  = (3)*20    eq1

       (5)(-3)x - (5)(2)y  =  (5)(-12)     eq2

rewriting:

        15x - 15y  =  60    eq1

       -15x -10y  = -60    eq2

    --------------------------------------    add the equations

          0   - 25y    = 0

               y  = 0

 

Then, put y=0 into either equation      (because we are finding the point that is on both lines, the intersection)

          5x - 5(0) = 20

          x = 4

 

Checking that the point (4,0) is on both lines:

 

eq1)    5(4) - 5(0) = 20

           20 = 20      yes

 

eq2)    (-3)(4)  - 2(0) = -12

           -12 = -12      yes