Question

1. a system of linear equations is shown.

$6x - 2y$
$y = 3x - 5$
which statement about the system is true?
options:
the system has one solution, $(-1, -8)$
the system has one solution, $(3, 4)$
the system has no solutions.
the system has infinitely many solutions.

Explanation:

Step1: Rewrite first equation

Rearrange $6x - 2y = 10$ to slope-intercept form:
Subtract $6x$ from both sides: $-2y = -6x + 10$
Divide by $-2$: $y = 3x - 5$

Step2: Compare the two equations

The second equation is $y = 3x - 5$, which is identical to the rearranged first equation.

Step3: Determine solution type

Identical linear equations overlap completely, so they have infinitely many points in common.

Answer:

The system has infinitely many solutions.