x= -8 and y= 1
Step-by-step explanation:
First, let's work on your first equation,3x+3y=-21
This means, see if it can be simplified at all before attempting to solve it.
Multiply x and 3
Multiply x and 1
The x just gets copied along.
The answer is x
x
3*x evaluates to 3x
Multiply y and 3
Multiply y and 1
The y just gets copied along.
The answer is y
y
3*y evaluates to 3y
3*x+3*y evaluates to 3x+3y
Because of the minus sign
21 becomes - 21
The answer is -21
So, all-in-all, your first equation can be written as: 3x+3y = -21
Now, let's work on your second equation,x+y=-7 x+y evaluates to x+y
Because of the minus sign
7 becomes - 7
The answer is -7
So, all-in-all, your second equation can be written as: x+y = -7
After this initial survey of the equations, the system of equations we'll set out to solve is:
3x+3y = -21 and x+y = -7
Let's start by solving 3x+3y = -21 for the variable x.
Move the 3y to the right hand side by subtracting 3y from both sides, like this:
From the left hand side:
3y - 3y = 0
The answer is 3x
From the right hand side:
The answer is -21-3y
Now, the equation reads:
3x = -21-3y
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.
The last step is to divide both sides of the equation by 3 like this:
To divide x by 1
The x just gets copied along in the numerator.
The answer is x
3x ÷ 3 = x
To divide -21-3y by 3
divide each term in -21-3y by 3 term by term.
-21 ÷ 3 = -7
To divide y by 1
The y just gets copied along in the numerator.
The answer is y
-3y ÷ 3 = -y
The solution to your equation is:
x = -7-y
Next, let's solve x+y = -7 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 -7-x
Now, the equation reads:
y = -7-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=-7-y, in for x everywhere it occurs in
y=-7-x.
This gives y=-7-(-7-y). Now all we have to do is solve this for y,to have our first solution.
Because of the minus sign
7 becomes - 7
The answer is -7
Because of the minus sign
7 becomes - 7
The answer is -7
-7-y evaluates to -7-y
-7 - -7 = 0
The answer is y
-7-(-7-y) evaluates to 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 0
Now, the equation reads:
0 = 0
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.
0 ÷ 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=-7-y.
This gives x=-7-(1). Now, simplify this.
Because of the minus sign
7 becomes - 7
The answer is -7
-7-(1) evaluates to -8
x= -8
