Question

How do you solve $3x - y = 9$ and $2x + y = 6$?

Answer 1

Hint: Here we are given two equations and there are two variables in it. Here we will use elimination method to find the values for the variables “x” and “y”.

Complete step-by-step solution:
Take the given two equations.
$3x - y = 9$ …. (A)
$2x + y = 6$ ….. (B)
Add equation (A) and (B), like terms with the same value and opposite sign cancel each other.
$ \Rightarrow 3x + 2x = 9 + 6$
Simplify the above equation.
$ \Rightarrow 5x = 15$
Term multiplicative on one side if moved to the opposite side, then it goes to the denominator.
$ \Rightarrow x = \dfrac{{15}}{5}$
Find the factors from the numerator part of the equation.
$ \Rightarrow x = \dfrac{{5 \times 3}}{5}$
Common factors from the numerator and the denominator cancel each other. Therefore remove from the numerator and the denominator.
\[ \Rightarrow x = 5\]
Place the value of “x” in the equation (A)
$3(5) - y = 9$
Simplify the above equation-
$15 - y = 9$
Move all the constants on one side of the equation and variables on the opposite side. When you move any term from one side to another, the sign of the term also changes. Positive terms become negative and vice-versa.
$15 - 9 = y$
Simplify the above equation.
$6 = y$
This can be re-written as –
$ \Rightarrow y = 6$
Hence, the required solution is:
$(x,y) = (5,6)$

Note: Be careful about the sign convention when you move any term from one side to another and also while simplification. While doing simplification remember the golden rules-
i) Addition of two positive terms gives the positive term
ii) Addition of one negative and positive term, you have to do subtraction and give signs of bigger numbers whether positive or negative.
iii) Addition of two negative numbers gives a negative number but in actual you have to add both the numbers and give a negative sign to the resultant answer.