Question

What is the solution to the system of equations?
x+y = 6
x=y +5

Answer 1

x+y=6 and
x+y=5 for the variables x and y.
First, let's work on your first equation,x+y=6

This means, see if it can be simplified at all before attempting to solve it.
x+y evaluates to x+y

So, all-in-all, your first equation can be written as: x+y = 6

Now, let's work on your second equation,x+y=5 x+y evaluates to x+y

So, all-in-all, your second equation can be written as: x+y = 5

After this initial survey of the equations, the system of equations we'll set out to solve is:
x+y = 6 and x+y = 5
Let's start by solving x+y = 6 for the variable x.
Move the y to the right hand side by subtracting y from both sides, like this:
From the left hand side:
y - y = 0

The answer is x

From the right hand side:
The answer is 6-y


Now, the equation reads:
x = 6-y
To isolate the x, we have to divide both sides of the equation by the other variables
around the x on the left side of the equation.

and this is the final solution to your equation.

Next, let's solve x+y = 5 for the variable y.
Move the x to the right hand side by subtracting x from both sides, like this:
From the left hand side:
x - x = 0

The answer is y

From the right hand side:
The answer is 5-x


Now, the equation reads:
y = 5-x
To isolate the y, we have to divide both sides of the equation by the other variables
around the y on the left side of the equation.

and this is the final solution to your equation.

Now, plug the earlier result, x=6-y, in for x everywhere it occurs in
y=5-x.

This gives y=5-(6-y). Now all we have to do is solve this for y,to have our first solution.
6-y evaluates to 6-y
5 - 6 = -1

The answer is -1+y

5-(6-y) evaluates to -1+y


Move the y to the left hand side by subtracting y from both sides, like this:
From the left hand side:
y - y = 0

The answer is 0

From the right hand side:
y - y = 0

The answer is -1


Now, the equation reads:
0 = -1
To isolate the y, we have to divide both sides of the equation by the other variables
around the y on the left side of the equation.

The last step is to divide both sides of the equation by 0 like this:

Sorry, can't divide by zero! Stop! Everything below this line is wrong.

0 ÷ 0 = 1


Sorry, can't divide by zero! Stop! Everything below this line is wrong.

-1 ÷ 0 = 1

The solution to your equation is:
1 = 1

Lastly, to find the solution for x, we plug this answer for y into the earlier result that
x=6-y.
This gives x=6-(1). Now, simplify this.
6-(1) evaluates to 5
x= 5

So, the solutions to your equations are:
x= 5 and y= 1

Answer 2

x=5 and y=1