Question

15. Use elimination to solve the system of equations given by7x + 23y = 12 and 3x + 23y = -8.A. no solutionB. infinitely many solutionsC. (1.25)D. (5, -1)16. Use elimination to solve the system of equations given by3x - 2y= 12 and 3x + 5y= 33A. no solutionB. (6,3)C. infinitely many solutionsD. (14,15)

Answer 1

Given the System of equations:

`\begin{gathered} \left\{ \begin{aligned}7x+23y=12 \\ 3x+23y=-8\end{aligned}\right. \\ \end{gathered}`

You can use the Elimination Method to solve it, following these steps:

1. You can multiply the second equation by -1.

2.Then you must add both equations.

Then:

`\begin{gathered} \left\{ \begin{aligned}7x+23y=12 \\ -3x-23y=8\end{aligned}\right. \\ _(\ldots\ldots\ldots\ldots\ldots...\ldots\ldots\ldots\ldots..) \\ 4x=20 \end{gathered}`

3. Solve for "x":

`\begin{gathered} x=(20)/(4) \\ x=5 \end{gathered}`

4. Substitute the value of "x" into any original equation and solve for "y":

`\begin{gathered} 7x+23y=12 \\ 7(5)+23y=12 \\ 35+23y=12 \\ 23y=12-35 \\ y=(-23)/(23) \\ y=-1 \end{gathered}`

So, the solution in the form (x,y), is:

`(5,-1)`

Therefore, the answer is OPTION D.