Question

How do you solve the equation for y, given $y + 7x = 9$then find the value for each value of x:$ - 1,0,4?$

Answer 1

Hint: Here we are given an equation with two variables and also given values for “x” so here we will place the value for “x” to get the value for “y”. First of all we will frame the equation in terms of “y”.

Complete step-by-step solution:
Take the given equation: $y + 7x = 9$
Make the required term “y” as the subject and move the term 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.
$ \Rightarrow y = 9 - 7x$ …. (A)
i) Place $x = ( - 1)$
In the equation (A)
$ \Rightarrow y = 9 - 7( - 1)$
When there is a negative sign outside the bracket then the sign of the term inside the bracket also changes.
$ \Rightarrow y = 9 + 7$
Simplify the above equation
$ \Rightarrow y = 16$
ii) Place $x = 0$
In the equation (A)
$ \Rightarrow y = 9 - 7(0)$
Zero multiplied with anything gives the resultant value as zero.
$ \Rightarrow y = 9 - 0$
Simplify the above equation
$ \Rightarrow y = 9$
iii) Place $x = 4$
In the equation (A)
$ \Rightarrow y = 9 - 7(4)$
When there is a negative sign outside the bracket then the sign of the term inside the bracket also changes.
$ \Rightarrow y = 9 - 28$
Simplify the above equation, when you simplify between one positive term and one negative term you have to do subtraction and give sign of bigger number.
$ \Rightarrow y = - 19$
Hence the required answer is
$( - 1,16),\;{\text{(0,9), (4, - 19)}}$

Note: Always be careful about the sign convention while opening the brackets and simplification. Remember the below rules -
i) Product of two positive terms gives resultant value in positive.
ii) Product of two negative terms gives resultant value in positive.
iii) Product of one positive and one negative term gives value in negative.