Question

4
$x - 3y = -15$
$x = 3$
$y = 2x - 4$
$6x - 3y = 12$
$y = 2x - 4$
$6x - 3y = 12$
$6x-3(2x-4)=12$
$6x-6x+12=12$
$12=12$

Explanation:

Step1: Substitute $y$ into second equation

Substitute $y=2x-4$ into $6x-3y=12$:
$$6x - 3(2x - 4) = 12$$

Step2: Expand and simplify the equation

$$6x - 6x + 12 = 12$$
$$12 = 12$$

Step3: Interpret the result

The simplified equation is a true statement with no variables left, meaning the two equations represent the same line, so there are infinitely many solutions.

Answer:

Infinitely many solutions (all points on the line $y=2x-4$)