Solving problems using the principles of Algebra can be fun only if a little care is taken to register the correct sign of either a number, or an alphabet or a combination of both. The correct signs should be assigned to the numbers as per the rules of Algebra. The rules written in textbook shall be followed with due consideration. Algebra 1 text-book is very useful in the sense that it not only provides the solution but it also provides the detailed description of basic knowledge to do or solve the task or problem.
Let us take some examples from Algebra 1 text for our better understanding purpose.
Example 1:- Solve (3x-7y+6z) – (x-7y-4z)
First step is to open the parentheses with due consideration to the negative sign.
(Explanation: - Presence of a negative sign before the parentheses alters the signs of all the numbers inside the second parentheses so x becomes –x, -7y becomes +7y, -4z becomes +4z. Or in other words if there is a –ve sign before the parentheses it is same as multiplying each number inside the parentheses by -1.)
Now we need to combine the same variables,
Find x and y,
If 4x+ 2y=16 and x + y =1
Tw equations are:-
4x+ 2y=16 …..equation
x + y =1 ….. equation 2
Now multiply equation 2 with 2 and then subtract from equation 1
4x+2y – 2x- 2y = 16 -2
2x = 14
Therefore x = 7
By substituting the value of x =7 in equation 2, we will get
7+y = 1
y = -6
So x = 7 and y = -6 is the solution