the solution to the system of equation below is (-2, -1). 2x - 3y = -1 11x - 9y = -13 when the first…

the solution to the system of equation below is (-2, -1). 2x - 3y = -1 11x - 9y = -13 when the first equation is multiplied by -3, the sum of the two equations is equivalent to 5x = -10. which system of equations will also have a solution of (-2, -1)? 5x = -10 11x - 9y = -13 2x + 9y = -1 11x - 9y = -13 -6x + 9y = -1 11x - 9y = -13

the solution to the system of equation below is (-2, -1). 2x - 3y = -1 11x - 9y = -13 when the first equation is multiplied by -3, the sum of the two equations is equivalent to 5x = -10. which system of equations will also have a solution of (-2, -1)? 5x = -10 11x - 9y = -13 2x + 9y = -1 11x - 9y = -13 -6x + 9y = -1 11x - 9y = -13

Answer

Answer:

A. $5x=-10$, $11x - 9y=-13$

Explanation:

Step1: Recall equivalent - system concept

Two systems of equations are equivalent if they have the same solutions. Given that multiplying the first equation $2x - 3y=-1$ by $-3$ gives $-6x + 9y = 3$. When added to $11x-9y=-13$, we get $( - 6x+9y)+(11x - 9y)=3+( - 13)$, which simplifies to $5x=-10$. The system with $5x=-10$ and $11x - 9y=-13$ is equivalent to the original system in terms of the solution.

Step2: Check other options

For the system $2x + 9y=-1$, $11x - 9y=-13$, adding the two equations gives $13x=-14$, which is not equivalent to the original system. For the system $-6x + 9y=-1$, $11x - 9y=-13$, adding gives $5x=-14$, which is also not equivalent. So the correct system is $5x=-10$, $11x - 9y=-13$.