Question

If $y + 7x = 3x - 2y + 28$. If x = 0, what is the value of y.?
A.$\dfrac{{28}}{3}$
B.9
C.7
D.10

Answer 1

Hint: A linear equation is any equation that can be written in the form $ax + by + c = 0$.
Where a and b are real numbers and x and y are variables. This form is sometimes called the standard form of a linear equation in two variables.
If the equation contains any fraction use the least common denominator. To clear the fractions, we will do this multiplying both sides of the equation by the LCD.

Complete step-by-step answer:
Step 1 consider the equation
$y + 7x = 3x - 2y + 28$; if x = 0 i.e. we put the value of x in the given equation and find the value of y. The given equation is a linear equation in two variables x and y.
In the left hand side of the given equation, the coefficient of variable x is 7 and the coefficient of variable y is 1.
In the right hand side of the given equation, the coefficient of variable x is 3 and the coefficient of variable y is 2 and 28 is constant value.
Step2. Firstly we have to simplify both sides of the equation. This means clearing out any parentheses and combining like terms. So, we get all the terms with the variable in terms on one side of equations and all the consonants on the other side.
i.e. $y + 7x - 3x + 2y = 28.....................(i)$
Here, in the left hand side of the given equation both the terms of variable y and variable x remains its position. But in the right hand side of the given equation, the term 3x taken in the left hand side is considered as negative terms. Similarly, term -2y takes in the left hand side, so it will be considered as a positive term. The constant value 28 remains its position on the right hand side.
Step 3. Now, put the value of x = 0 in (I) equation.
$\Rightarrow$ $y + 7(0) - 3(0) + 2y = 28$
If any real number multiplied by zero, we get value zero. So,
$\Rightarrow$ $y + 0 - 0 + 2y = 28$
$\Rightarrow$ $y + 2y = 28$
Here, only two terms are left on the left side of variable y .
$\Rightarrow$ 3y = 28
If we add y and 2y, we get 3y. Here 3 is the coefficient of y.
Now, if we find the value of y so, take the coefficient 3. The denominator of 28 on the right side.
  $y = \dfrac{{28}}{3}$
So, the value of y is 28/3.
Hence, option A is the right answer.


Note: We would probably also acknowledge that provided equation we don’t have any division by zero. Linear equations will have exactly one solution. We will never get more than one solution and the only time that we won’t get any solution is if we run across a division with zero problems with the solution.