Question

15 mark for review -15x + 25y = 65 one of the two equations in a system of linear equations is given. the system has infinitely many solutions. which of the following could be the second equation in the system? a 12x + 20y = 52 b 12x + 20y = -52 c -12x + 20y = 52 d -12x + 20y = -52

Explanation:

Step1: Simplify the given equation

Divide $-15x + 25y=65$ by $- 5$. We get $3x - 5y=-13$.

Step2: Check each option

For option A: Divide $12x + 20y = 52$ by $4$, we have $3x+5y = 13$, not equivalent.
For option B: Divide $12x + 20y=-52$ by $4$, we get $3x + 5y=-13$, not equivalent.
For option C: Divide $-12x + 20y = 52$ by $-4$, we obtain $3x - 5y=-13$, equivalent to the simplified given - equation.
For option D: Divide $-12x + 20y=-52$ by $-4$, we have $3x - 5y = 13$, not equivalent.

Answer:

C. $-12x + 20y = 52$