Chapter 6, Problem 8PT

To determine

To solve: The system of equations using elimination method.

Answer to Problem 8PT

The option B is correct.

Explanation of Solution

Given information:

The given system of equations is

  $6x-4y=6$

  $-6x+3y=0$

The Solution is A. $\left(5,6\right)$ B $\left(-3,-6\right)$ C $\left(1,0\right)$ D $\left(4,-8\right)$

Concept used:

In elimination method, one variable is eliminated by making the coefficient of that variable equal in both the equations.

Calculations:

The given equations are

  $6x-4y=6$  ...... (1)

  $-6x+3y=0$   ...... (2)

As the coefficients of variable “ x ” in both equations are identical and of opposite sign so adding equations (1) and (2)

  $\left(6x-4y\right)+\left(-6x+3y\right)=6+0$

  $\Rightarrow \left(6x-6y\right)+\left(-4y+3y\right)=6+0$

  $\Rightarrow 0-y=6$

  $y=-6$

Further, substituting value of y in equation (2)

  $-6x+3\left(-6\right)=0$

  $\Rightarrow -6x-18=0$

  $\Rightarrow -6x=18$

  $\Rightarrow x=\frac{18}{-6}=-3$

Thus, $x=-3$ , $y=-6$ is the solution of system of equations $6x-4y=6$ and $-6x+3y=0$ .

Hence, the option B is correct.

Conclusion:

The solution of system of equations $6x-4y=6$ and $-6x+3y=0$ is $x=-3$ , $y=-6$ , the option B is correct.