Question

Which system of linear equations has the same solution as the one shown below?

x - 4y &= -10
x + y &= 5

A) (5x=10), (x+y=5)
B) (-5y=-5), (x+y=5)
C) (-3x=-30), (x+y=5)
D) (-5y=-5), (x-4y=-10)

Answer 1

The system of linear equations which has the same solution as the given system x - 4y = -10 and x + y = 5 is D) -5y = -5, x - 4y = -10.

Step-by-step explanation:

The student is asking which system of linear equations has the same solution as x - 4y = -10 and x + y = 5. To find a system with the same solution, we want another system where the relationships between x and y are unchanged.

Looking at the options provided:

• A) 5x = 10 doesn't relate to y at all and thus isn't equivalent to x - 4y = -10.
• B) -5y = -5 implies y = 1, which if substituted into x + y = 5 will give us a solution for x, thus potentially aligning with our system.
• C) -3x = -30 simplifies to x = 10, which does not align with the original system.
• D) We have the same two equations as the original system and therefore the same solution.

Therefore, the correct answer is D) -5y = -5, x - 4y = -10.