Question

martina says that (2, -4) is a solution to the system. sai says there are infinitely many solutions.
( y = 4(x - 3) )
( y = 4x - 12 )
whose claim is correct? use the sketch tool if it helps with your thinking.
martina’s
sai’s
both
neither

Explanation:

Step1: Simplify the first equation

The first equation is \( y = 4(x - 3) \). Using the distributive property \( a(b - c)=ab - ac \), we get \( y = 4x - 12 \).

Step2: Compare the two equations

The second equation is \( y = 4x - 12 \). So both equations are identical. This means the system of equations represents the same line, and thus there are infinitely many solutions (all points on the line). Also, we can check if \( (2, - 4) \) is a solution. Substitute \( x = 2 \) and \( y=-4 \) into \( y = 4x - 12 \):
Left - hand side (LHS) \(= - 4\)
Right - hand side (RHS) \(=4\times2 - 12=8 - 12=-4\)
Since LHS = RHS, \( (2,-4) \) is a solution. So both Martina's and Sai's claims are correct.

Answer:

Both