Algebra Know-It-ALL

Then we can subtract 10 from each side to obtain this SI equation with w playing the role of
the dependent variable:

w= 7 v− 10

Make a first-degree equation

The second step involves substituting our “new name” for w into the equation we haven’t
touched yet, which in this case is the second original. That gives us

4 v+ 8(7v− 10) =− 40

The distributive law of multiplication over subtraction can be applied to the second addend
on the left side of the equals sign to get

4 v+ 56 v− 80 =− 40

Summing the first two addends in the left side of this equation gives us

60 v− 80 =− 40

Adding 80 to each side, we obtain

60 v= 40

This tells us that v= 40/60 = 2/3.

Plug the number into the best place

Now that we have solved for one of the variables, we can replace the resolved unknown with
its solution in any relevant equation containing both variables. The simplest approach is to use
is the SI equation we derived in the first step:

w= 7 v− 10

When we replace v by 2/3 here, we get

w= 7 × 2/3 − 10

Taking the product on the right side of the equals sign, and changing 10 into 30/3 to obtain
a common denominator, we come up with

w= 14/3 − 30/3

Now it’s a matter of mere arithmetic:

w= (14 − 30)/3

=−16/3

We’ve derived the solution to this system: v= 2/3 and w=−16/3.

Rename and Replace 259