Chapter 6, Problem 41SGR

To determine

To find: The system of equation using elimination.

Answer to Problem 41SGR

The solution is $x=1,y=-2$

Explanation of Solution

Given:

  $8x-5y=18$

  $6x+6y=-6$

Calculation:

Here the equation is:

  $8x-5y=18$........(1)

And,

  $6x+6y=-6$........(2)

The strategy is to solve the system of equations using elimination.

Multiply equation (1) by 6:

  $6\left(8x-5y\right)=6\left(18\right)$

  $48x-30y=108$........(3)

Multiply equation (2) by 5:

  $5(6x+6y)=5(-6)$

  $30x+30y=-30$..........(4)

Add equation (3) with (4) to get:

  $\left(48x-30y)+(30x+30y\right)=108-30$

  $\text{78}x=78$

  $\frac{78x}{78}=\frac{78}{78}$

  $x\text{=1}$

From equation (2),

  $\text{6}\left(1\right)+6y=-6$

  $6+6y-6=-6-6$

  $\frac{6y}{6}=\frac{-12}{6}$

  $y=-2$

Hence, the solution is: $x=1,y=-2$

Conclusion:

Therefore, the solution is: $x=1,y=-2$