The depth of the bottom of the hole after the second day is 36 feet using addition operation.
<h3>What is addition?</h3>
In math, addition is the process of adding two or more integers together. Addends are the numbers that are added, while the sum refers to the outcome of the operation.
Given the depth on the first day is 26 ½ feet.
Depth on the second day = 9½ feet more than on the first day i.e. 9½ feet + depth on the first day
This implies, depth on the second day = 9½ + 26 ½
= 36 feet
Therefore, the depth of the bottom of the hole after the second day is 36 feet.
To solve by elimination, we want to <em>eliminate</em> a variable. To do this, we must make one variable cancel out.
First, we can see that both equations have 9x. To cancel out x, we must make <em>one</em> of the 9x's <em>negative</em>. To do this, multiply <em>each term</em> in the equation by -1.
-1(9x + 6y = 123)
-9x - 6y = -123
This is one of your equations. Set it up with your other given equation.
9x + 4y = 97
-9x - 6y = -123
Imagine this is one equation. Since every term is negative, you will be subtracting each term.
9x + 4y = 97
-9x - 6y = -123
___________
0x -2y = -26
-2y = -26
To isolate y further, divide both sides by -2.
y = 13
Now, to find x, plug y back into one of the original equations.
9x + 4(13) = 97
Multiply.
9x + 52 = 97
Subtract.
9x = 45
Divide.
x = 5
Check your answer by plugging both variables into the equation you have not used yet.
