Question

Solve the system using elimination- 8x + 6y = 24-16x - 7y = -28Show your work here:Solution

Answer 1

Given:

`\begin{gathered} -8x+6y=24 \\ -16x-7y=-28 \end{gathered}`

Using the elimination method,

`\begin{gathered} \text{Multiplying equation (1) by 2;} \\ -8x+6y=24\ldots\ldots\ldots\ldots\text{......}(1)*2 \\ -16x+12y=48\ldots\ldots\ldots\ldots\ldots\ldots\text{.}\mathrm{}(1)\text{new equation (1)} \\ -16x-7y=-28\ldots\ldots..\ldots\ldots\ldots..\mathrm{}(2) \\ \text{Subtracting equation (2) from (1);} \\ (1)-(2); \\ -16x-(-16x)+12y-(-7y)=48-(-28) \\ 12y+7y=48+28 \\ 19y=76 \\ y=(76)/(19) \\ y=4 \end{gathered}`

Substituting y into equation (1);

`\begin{gathered} -8x+6y=24 \\ -8x+6(4)=24 \\ -8x+24=24 \\ -8x=24-24 \\ -8x=0 \\ x=0 \end{gathered}`

Therefore, the solution is;

`(x,y)=(0,4)`

The solution is also shown graphically below;