Question

$y = -6x+2$
$-12x - 2y = -4$
how many solutions does this linear system have?
○ one solution: (0, 0)
○ one solution: (1, -4)
○ no solution
○ infinite number of solutions

Explanation:

Step1: Substitute $y$ into second equation

Substitute $y=-6x+2$ into $-12x-2y=-4$:
$-12x - 2(-6x+2) = -4$

Step2: Simplify the left-hand side

Expand and combine like terms:
$-12x +12x -4 = -4$
$-4 = -4$

Step3: Interpret the result

The equation is always true, meaning the two lines are identical, so there are infinitely many points that satisfy both equations.

Answer:

infinite number of solutions