Question

mandy solved this system of equations using elimination.
9x + 15y = 6
3y = -5x + 2
mandy says that the system has no solutions. is mandy’s statement true or false?
true
false

Explanation:

Step1: Rewrite the second equation

The second equation is \(3y = -5x + 2\). Let's rewrite it in standard form \(Ax + By = C\). Add \(5x\) to both sides: \(5x + 3y = 2\). Now, multiply this equation by 5 to make the coefficients of \(y\) match the first equation's \(y\) coefficient (15). So, \(5(5x + 3y)=5\times2\) which simplifies to \(25x + 15y = 10\).

Step2: Analyze the first equation

The first equation is \(9x + 15y = 6\). Now we have two equations:

1. \(9x + 15y = 6\)
2. \(25x + 15y = 10\)

Subtract the first equation from the second equation: \((25x + 15y)-(9x + 15y)=10 - 6\). Simplify the left side: \(25x - 9x+15y - 15y = 16x\), and the right side is \(4\). So, \(16x = 4\), which means \(x=\frac{4}{16}=\frac{1}{4}\). Since we can find a value for \(x\), we can substitute back to find \(y\), so the system has a solution. Therefore, Mandy's statement that the system has no solutions is false.

Answer:

False