First, let's work on your first equation,a+b=1.1
This means, see if it can be simplified at all before attempting to solve it.
a+b evaluates to
a+b
So, all-in-all, your first equation can be written as:
a+b =
1.1
Now, let's work on your second equation,a-b=1 a-b evaluates to
a-b
So, all-in-all, your second equation can be written as:
a-b =
1
After this initial survey of the equations, the system of equations we'll set out to solve is:
a+b =
1.1 and
a-b =
1
Let's start by solving
a+b =
1.1 for the variable a.
Move the
b to the right hand side by subtracting
b from both sides, like this:
From the left hand side:
b -
b =
0
The answer is
a
From the right hand side:
The answer is
1.1-b
Now, the equation reads:
a =
1.1-b
To isolate the a, we have to divide both sides of the equation by the
other variables
around the a on the left side of the equation.
and this is the final solution to your equation.
Next, let's solve
a-b =
1 for the variable b.
Move the
a to the right hand side by subtracting
a from both sides, like this:
From the left hand side:
a -
a =
0
The answer is
-b
From the right hand side:
The answer is
1-a
Now, the equation reads:
-b =
1-a
To isolate the b, we have to divide both sides of the equation by the
other variables
around the b on the left side of the equation.
The last step is to divide both sides of the equation by
-1 like this:
To divide
b by
1
The
b just gets copied along in the numerator.
The answer is
b
-b ÷
-1 =
b
To divide
1-a by
-1
divide each term in
1-a by
-1 term by term.
1 ÷
-1 =
-1
To divide
a by
1
The
a just gets copied along in the numerator.
The answer is
a
-a ÷
-1 =
a
The solution to your equation is:
b =
-1+a
Now, plug the earlier result, a=1.1-b, in for a everywhere it occurs in
b=-1+a.
This gives b=-1+(1.1-b). Now all we have to do is solve this for b,to have our first solution.
Because of the minus sign
1 becomes -
1
The answer is
-1
1.1-b evaluates to
1.1-b
-1 +
1.1 =
0.1
The answer is
0.1-b
-1+(1.1-b) evaluates to
0.1-b
Move the
-b to the left hand side by adding
b to both sides, like this:
To the left hand side:
b +
b =
2b
The answer is
2b
To the right hand side:
-b +
b =
0b
The answer is
0.1
Now, the equation reads:
2b =
0.1
To isolate the b, we have to divide both sides of the equation by the
other variables
around the b on the left side of the equation.
The last step is to divide both sides of the equation by
2 like this:
To divide
b by
1
The
b just gets copied along in the numerator.
The answer is
b
2b ÷
2 =
b
0.1 ÷
2 =
0.05
The solution to your equation is:
b =
0.05
Lastly, to find the solution for a, we plug this answer for b into the earlier result that
a=1.1-b.
This gives a=1.1-(0.05). Now, simplify this.
1.1-(0.05) evaluates to
1.05
a=
1.05
So, the solutions to your equations are:
a= 1.05 and b= 0.05