Solving by subsitution

Question

x-y=0

-6x+5y=4

 

Can anyone help me with this problem? Im really struggling.

Answer 1

John,

     Since x-y=0 then x=y from the first equation

 

Putting x=y in the second equation gives -6y+5y=4 so y=-4 and x=-4.

 

The idea is to solve one of the equations for one of the unknowns and substuite that relationship in the second equation to eliminate one of the unknowns. Then solve that equation for the remaining unknown. 

 

Hope this helps

Jim

Answer 2

For this question you have to solve the equations substituting one equation into the other. The easiest way will be to manipulate the first equation:

 

x - y = 0  ----> x - y (+ y) = 0 (+ y) --->  x = y

 

From here you substitute the first equation into the second equation. For this example, l'll substitute "y" out of the equation:

 

-6x + 5y = 4  ---->   -6x + 5(x) = 4

 

                               -x = 4

                                x = -4

 

Take this answer back into the first equation:

 

y = x

 

y = -4

 

 

Hope this helps you out!

Answer 3

OK. Substitution can work well with a problem like this. What you do is take one of the two equations, solve that equation for one of the two variables in terms of the other, and substitute into the other equation.

Now, it works well here because the first equation is x - y = 0.

 

Solve that and you get x = y.

 

Now, substitute for either x or y in the other equation.

 

-6x + 5y = 4.

 

OK. Substitute x for y.

 

-6x + 5x = 4

-x = 4

x = -4

 

And y = -4 too.

 

This is a good problem to get your feet wet with substitution. Many problems are much harder, but the routine is the same.

 

Cheers!