Chapter 6, Problem 11MCQ

To determine

To solve: The given system of linear equation using substitution method.

Answer to Problem 11MCQ

The solution of given system of equations is $x=7$ and $y=-1$ .

Explanation of Solution

Given information:

The given system of equations is

  $x+y=6$

  $x-y=8$ .

Concept used:

In substitution expression for one variable from an equation is substituted in other. And the so obtained single variable equation is solved.

Calculations:

The given system of equation is

  $x+y=6$  ...... (1)

  $x-y=8$  ...... (2)

The equation (2) can be written as

  $x=8+y$  ...... (3)

Now, substituting expression for y from equation (3) into equation (1)

  $x+y=6$

  $\Rightarrow 8+y+y=6$

  $\Rightarrow 2y=6-8$

  $\Rightarrow 2y=-2$

  $\Rightarrow y=\frac{-2}{2}=-1$

Further, $x=8+y$

  $\Rightarrow x=8-1$

  $\Rightarrow x=7$

Thus, we have $x=7$ and $y=-1$ .

Conclusion:

The solution of given system of equations is $x=7$ and $y=-1$ .