How do you solve simultaneous equations using the substitution method ?x=y 6x-2y=10 x=-y 3x-6y=36

Substitution Method is used to solve simultaneous equations, as given above. To solve simultaneous equations the following steps should be taken:

Label the equations as i and ii,

x=y         ------(i)   

6x-2y=10 ------(ii)

The next step is to isolate one variable from any equation, which has been done already as x=y.

After this step input the value of x in eq(ii) and solve to get the value of y:

6x-2y=10 ------(ii)

6y-2y=10

4y=10

4y/4=10/4         divide both sides by 4

y=2.5

After this we would have to input this value in equation ii, but since it has already been determined that x=y we can say that x=2.5 as well.

x=2.5

y=2.5

To further check the answers input both values in eq(ii)

6x-2y=10

6(2.5)-2(2.5)=10

15-5=10

10=10

LHS=RHS proved.

The same steps are to be followed in this one:

x=-y         -------(i)  

3x-6y=36  -------(ii)

Input the value of x in eq(ii)

3x-6y=36

3(-y)-6y=36

-3y-6y=36

-9y=36

-9y/-9=36/-9        divide both sides by -9

y=-4

Now since both value are equal only their signs are different i.e. x=-y therefore x=4. 

Input both value in eq(ii) to check if they are correct:

3x-6y=36  -------(ii)

3(4)-6(-4)=36

12+24=36

36=36

LHS=RHS proved.