Question

Find the value of $x$ if \[x + y = 5\] and \[x - y = 7\]

Answer 1

Hint: This question can be solved in various methods.
Below mentioned are the various methods:
1.Graphing
2.Substitution method
3. elimination method
are the commonly used methods to solve.
We will be using substitution method to solve this question.
From the given equations find the value of any one of the variables and substitute the value in the other equation.

Complete step-by-step answer:
By using Substitution method:
Let \[x + y = 5\] _______ (1) and
\[x - y = 7\] _______ (2)
Find the value of y from equation \[(1)\] and substitute in equation \[(2)\].
From equation \[(1)\]
\[x + y = 5\]
Transforming $x$ to the other side of equation
\[y = 5 - x\]_______ (3)
Substitute equation \[(3)\] in equation \[(2)\]
\[x - y = 7\]
Substitute the value of y found in equation 3.
\[x - (5 - x) = 7\]
Multiplying negative sign to remove bracket
\[x - 5 + x = 7\]
\[2x - 5 = 7\]
Negative term taken other side of equal to as positive
\[2x = 7 + 5\]
\[2x = 12\]
Dividing by 2 on both sides.
\[x = 6\] So, the value of x=6.

Additional Information:
An equation is said to be linear equation in two variable if it is written in the form , where a, b & c are real numbers and the coefficient of x and y i.e. a and b respectively are not equal to zero
Solution of linear equations are in two variables. The solution of line equations in two variables is particular in the graph, such that when x-coordinate is multiplied by a and y-coordinate is multiplied by b. A linear equation in two variables has infinitely many solutions.

Note: Alternative method:
First arrange both equations in standard form, we get :
\[x + y = 5\]
And,
\[x - y = 7\]
The coefficients of y are \[1\] and \[ - 1\], i.e. both are the same. Adding equation \[(1)\] and equation \[(2)\]
We have
\[\begin{gathered}
  \begin{array}{*{20}{c}}
  x& + &{y = }&5
\end{array} \\
  \underline {x\,\,\,\,\,\, - \,\,\,\,y\,\, = \,\,\,\,\,7} \\
  2x\,\,\, + \,\,\,\,0\,\,\,\, = 12 \\
\end{gathered} \]
\[2x = 12\]
\[x = \dfrac{{12}}{2}\]
\[x = 6\]
Hence, the value of \[x = 6\]