Solve The system of equations using elimination.

Question

2x+7y=1

2x-4y=12

Answer 1

2x = 1 - 7y = 12 + 4y

 

11y = -11 ------> y = -1 and x = 4

Answer 2

Elimination means that you find a way to add or subtract the equations together, in such a way that one of the variables is eliminated.  That means you want the coefficients of one of the variables to be the same in both equations, or if not the same then the same except for sign.

 

Sometimes you have to multiply one or both of the equations by some constant in order to make that possible.

 

In this case, the coefficient of the x term is the same in both equations.  So you can subtract one equation from the other and the x's will disappear.  Then you'll have an equation for y alone that you can solve:

2x + 7y = 1
2x - 4y = 12

 

Subtract the second equation from the first:

2x + 7y - (2x -4y) = 1 - 12

2x + 7y - 2x + 4y = -11

11y = -11

y = -1

 

Once you have the solution for one of the variables, you can substitute it back into one of the equations and get the solution for the other variable.  Let's substitute -1 for y in the first equation:

 

2x + 7y = 1

2x + 7(-1) = 1

2x - 7 = 1

2x = 8

x = 4

 

So the solution is x = 4, y = -1