Chapter 6, Problem 10MCQ

To determine

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

Answer to Problem 10MCQ

The solution of given system of equations is $x=-12$ and $y=21$ .

Explanation of Solution

Given information:

The given system of equations is

  $y=-2x-3$

  $x+y=9$ .

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

  $y=-2x-3$  ...... (1)

  $x+y=9$  ...... (2)

Now, substituting expression for y from equation (1) into equation (2)

  $x+\left(-2x-3\right)=9$

  $\Rightarrow -x-3=9$

  $\Rightarrow -x=9+3=12$

  $\Rightarrow x=-12$

Further, $y=-2x-3$

  $\Rightarrow y=-2\times \left(-12\right)-3$

  $\Rightarrow y=24-3=21$

Thus, we have $x=-12$ and $y=21$ .

Conclusion:

The solution of given system of equations is $x=-12$ and $y=21$ .