Question

solve the system using addition/elimination method. if there is exactly one solution, write as an ordered pair. if not, choose one of the other options.
\\(\

$$\begin{cases}5x + 6y=-19\\-10x - 12y = 38\\end{cases}$$

\\)
one solution:
no solution
infinite number of solutions
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Explanation:

Step1: Multiply first - equation by 2

Multiply the equation \(5x + 6y=-19\) by 2. We get \(2(5x + 6y)=2\times(-19)\), which simplifies to \(10x + 12y=-38\).

Step2: Rewrite the second - equation

The second equation is \(-10x-12y = 38\), which can be rewritten as \(10x + 12y=-38\) (by multiplying both sides by - 1).

Step3: Analyze the relationship between the equations

Since the two equations \(10x + 12y=-38\) and \(10x + 12y=-38\) are identical, the system has an infinite number of solutions.

Answer:

Infinite number of solutions