Question

y = -6x + 2\
-12x - 2y = -4\
how many solutions does this linear system have?\
\bigcirc one solution (0, 0)\
\bigcirc one solution (1, -4)\
\bigcirc no solution\
\bigcirc 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: Analyze the result

The equation simplifies to a true statement with no variables, meaning the two lines are identical.

Answer:

infinite number of solutions