Question

solve the system using addition/elimination method. if there is exactly one solution, write as an ordered pair. otherwise, choose one of the other options.
\\(\

$$\begin{cases}-2x - 8y = 28 \\ -3x - 12y = 44\\end{cases}$$

\\)
one solution:
no solution
infinite number of solutions
question help: video 1 video 2

Explanation:

Step1: Multiply equations for elimination

Multiply the first - equation $-2x - 8y=28$ by 3 and the second - equation $-3x - 12y = 44$ by 2.
The first equation becomes $3(-2x - 8y)=3\times28$, which simplifies to $-6x-24y = 84$.
The second equation becomes $2(-3x - 12y)=2\times44$, which simplifies to $-6x-24y = 88$.

Step2: Subtract the equations

Subtract the first new - equation from the second new - equation:
$(-6x - 24y)-(-6x - 24y)=88 - 84$.
$0=4$ (This is a contradiction).

Answer:

No solution