Chapter 6, Problem 9MCQ

To determine

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

Answer to Problem 9MCQ

The solution of given system of equations is $x=4$ and $y=7$ .

Explanation of Solution

Given information:

The given system of equations is

  $y=x+4$

  $2x+y=16$ .

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

  $y=x+4$  ...... (1)

  $2x+y=16$  ...... (2)

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

  $2x+\left(x+4\right)=16$

  $\Rightarrow 3x+4=16$

  $\Rightarrow 3x=16-4=12$

  $\Rightarrow x=\frac{12}{3}=4$

Further, $y=x+4$

  $\Rightarrow y=3+4=7$

Thus, we have $x=4$ and $y=7$ .

Conclusion:

The solution of given system of equations is $x=4$ and $y=7$ .