Question

How do you solve the following system $ y = 4x - 13,y - 3x = - 2 $ ?

Answer 1

Hint: In order to determine the solution of a given system of equations having two variables, use the method of elimination of term by eliminating the $ y $ term by making the mod of coefficient of $ y $ in both the equations equal. Then apply the operation of addition or subtraction between the equation to eliminate $ y $ term. Solve the result for $ x $ and put the obtained value of $ x $ in any of the equations given to get the value of $ x $.

Complete step by step solution:
 We are given pair of linear equation in two variables \[y = 4x - 13,y - 3x = - 2\]
 $ y = 4x - 13 $ ---(1)
\[y - 3x = - 2\]
Rewriting the above by transposing term containing $ x $ toward right-hand side
\[y = 3x - 2\]----(2)
In order to solve the system of equations, we have many methods like, substitution, elimination of term, and cross-multiplication.
Here we will be using an elimination method to eliminate the term having $ y $ from both the equations.
And to do so we have to first make the mod of coefficient of $ y $ in both the equation equal to each.
As we can clearly see that the mod of coefficient of $ y $ in both the equations are already equal.
Now subtracting both the equation, we get
 $
\Rightarrow y - y = 4x - 13 - \left( {3x - 2} \right) \\
  0 = 4x - 13 - 3x + 2 \;
  $
Combining like terms we get
 $ x - 11 = 0 $
Solving the equation for variable $ x $
 $ x = 11 $
Hence, we have obtained the value of $ x = 11 $ .
Now putting this value of $ x $ in the equation (2) to get the value of \[y\]
\[
\Rightarrow y = 3\left( {11} \right) - 2 \\
  y = 33 - 2 \\
  y = 31 \;
 \]
Therefore, the solution of system of given equations is $ x = 11,y = 31 $
So, the correct answer is “ $ x = 11,y = 31 $ ”.

Note: Linear Equation in two variable: A linear equation is a equation which can be represented in the form of $ ax + by + c $ where $ x $ and $ y $ are the unknown variables and c is the number known where $ a \ne 0,b \ne 0 $ .
The degree of the variable in the linear equation is of the order 1.One must be careful while calculating the answer as calculation error may come.